Operaphiles who saw the ads must have wondered about that. Perhaps Bizet's name was included so people wouldn't confuse this with the flamenco-style ''Carmen'' movie put out previously by Carlos Saura. But why was the second word left unitalicized, or unsurrounded by quotation marks of its own? Did someone in the publicity department make a boo-boo? Or was this a suggestion that Rosi's interpretation of Carmen - and presumably of ''Carmen'' as well - was in some significant way faithful to Bizet's intentions?

Three years earlier, British director Peter Brook had unveiled his ''La Tragédie de Carmen,'' an adventurous theater piece that, although flavored with Bizet's music and generally respectful of Bizet's plot, was to a large extent based on the ''Carmen'' novella that Prosper Mérimée published in France 30 years before the opera's premiere in 1875. Indeed, so far removed from the familiar operatic figure was Brook's leading lady that Brook might well have called his show ''Mérimée's Carmen.''

So maybe Rosi was reacting to Brook's version.

Rosi's Carmen (played by Julia Migenes-Johnson) was about a zillion times sexier than the typical Carmen one sees in the opera house. All things considered, though, it was primarily her sweaty, dusty cleavage that distinguished her from the traditional character. She was a free spirit and a man-eater, yet she loved her Don Jose - for a while - with an intensity that fairly burned up the screen. As almost all operatic Carmens have been, she was a romantic figure, a flesh-and-blood woman for whom the expression of passionate emotions in song seemed almost natural. At least, that's what Carmen has been for as long as most of us can remember. In that sense, Rosi's Carmen was Bizet's Carmen.

Or was she?

The question comes up because Colin Graham, who is directing the ''Carmen'' that opens Opera Theatre of St. Louis' 1987 season on Saturday, says that his Carmen is Bizet's Carmen.

As he usually does for his productions here, Graham has written an interesting essay on ''Carmen'' for the Opera Theatre program booklet. He does not mention the Rosi film, but perhaps he alludes to it in his sweeping sentence about ''most productions (of 'Carmen') since the first one.'' Most of them, Graham writes, have been bothered by ''a serious mistake,'' the mistake of ignoring the characterizations in the opera's literary source.

''Don Jose is usually portrayed as just a dumb cluck,'' Graham said Monday evening in a lecture at Webster University, ''and Carmen is usually played as a beautiful woman with a rose in her teeth who flirts with every man in sight. That has always troubled me, for surely these could not have been the characters that attracted Bizet to the story in the first place.

''In fact, the Carmen and Don Jose of the novella are quite different from the Carmen and Don Jose of the opera. There are good reasons for their transformation; some of them are musical and theatrical, and some of them have to do with the conventions of the Opera Comique in Paris where 'Carmen' was first performed. Of course, it would be a mistake for a director to think he could simply lift characters from the pages of the book and put them on the stage. But one does have to consider the bedrock. I assure you, our Carmen will be Bizet's Carmen, not Mérimeé's, but it will be Bizet's Carmen as inspired by Mérimée.''

For people who have already been seduced by the operatic Carmen - in other words, just about everyone who's been exposed to her charms at least once - this has to be confusing. Who is Carmen, really? Who, at least, is the literary Carmen who apparently will loom large in Graham's production?

She's not a nice person, that's for sure.

The archaeologist offers the first description. Carmen is ''petite, young,'' with ''a shapely figure and very big eyes,'' he says. He goes with her to have his fortune told, whereupon he observes: ''Hers was a strange, wild beauty, a face that at first was astonishing, but which was unforgettable. Her eyes especially had an expression both voluptuous and fierce, such as I have never found since in any human look.'' When an irritated Don Jose bursts in on the fortune-telling session, Carmen grows ''gradually more excited.'' ''Her eyes became bloodshot and terrified,'' the archaeologist says. ''Her features contracted and she stamped her foot.'' Then she steals the archaeologist's watch.

Jose's account of his first glimpse of Carmen is juicier: ''She was wearing a very short red skirt which revealed white silk stockings with more than one hole in them, and dainty red morocco leather shoes tied with flame-colored ribbons. She wore her mantilla lowered in order to show off her shoulders and a big bouquet of acacia at the opening of her blouse. She also had an acacia flower in the corner of her mouth, and she walked swaying her hips like a filly on a Cordova stud farm. In my region, a woman decked out in a costume like that would have caused people to make the sign of the cross.''

''She was always lying,'' Jose tells the archaeologist. ''I don't know if that girl has ever spoken a word of truth in her whole life. But when she spoke, I believed her.''

Later he says: ''If there really are any witches, sir, that girl certainly was one!'' Later: ''She said: 'Do you know what, my boy? I think I love you a little. But that can't last. A dog and a wolf don't make a good household for long. . . . You've met up with the Devil, yes, the Devil - he's not always black, you know.' ''

Later, when the story of the affair reaches its stormy peak: ''I said: 'I'm tired of killing all your lovers. You're the one I'll kill next time.' She looked at me with a fixed stare in her wild eyes, and then she said to me: 'I've always thought you'd kill me. The very first time you saw me, I'd just met a priest at the door of my house. And tonight, as we were leaving Cordova, didn't you notice anything? A rabbit ran across the road between your horse's feet. That is fate!' ''

And finally, after Jose tells the archaeologist how he stabbed Carmen to death and buried her body in the woods: ''Poor child! It is the gypsies who are to blame for having brought her up that way!''

But the character had to get sweetened if she was to be presented on the stage of the Opera Comique. And she was sweetened a lot more after Bizet died, just three months after the opera's scandalous - and thus disasterous - premiere.

Over the years Carmen has evolved into a character who is both attractive and who elicits sympathy; in most productions I've seen it's Jose who's been the villain, not just a dumb cluck but a violence-prone hot-head who can't handle the fact that Carmen has found a new boyfriend.

That has to be counted among the greatest understatements in the entire operatic literature. The composer who set that line indeed wrote an interesting opera about her, and it's one of the most interesting operas of the 20th century.

Alban Berg's ''Lulu'' was controversial even before its first performance in 1937. It remained controversial after its first complete performance in 1979. In the last eight years the full three-act version of ''Lulu'' has had more than a dozen productions world-wide. But audiences still squirm in Lulu's presence. And directors still ponder her identity.

Who - or what - is Lulu?

Yuri Ljubimov first staged the three-act ''Lulu'' for the Teatro Regio in Turin, Italy, in 1983, and lately he's restaged the same production for the Chicago Lyric Opera. To arrive at his answer to the question, he follows up on a clue found early in Berg's libretto.

The opera begins with a rhymed prologue delivered by an animal tamer. ''You'll see a tiger who is ready to kill, a greedy bear, a monkey who abuses his talent,'' he says. ''You'll also see a serpent.'' The serpent, of course, is Lulu.

Berg's summary description of her (in Arthur Jacobs' translation) is worth quoting:

''She as the root of all evil was created,/To snare us, to mislead us she was fated,/And to murder, with no clue left on the spot. My sweetest beast, please don't be what you're not!/You have no right to seem a gentler creature,/Distorting what is true in woman's nature.''

Almost the entire cast is paraded on stage as those metaphoric lines are sung. All but the animal tamer stand behind a wall of bars. The wall is movable, and for most of the opera it lies flat on the floor. Only twice more is it hauled up: in the middle of Act II during a pantomime sequence that depicts Lulu's imprisonment, and at the very end, after Lulu has a brief but fatal encounter with Jack the Ripper. The bar image neatly underscores the opera's symmetrical dramatic structure; the plot deals with Lulu's rise and then her demise, and the pantomime (a three-minute silent film in the original 1937 production in Zurich) comes precisely at the turning point. The bar image also emphasizes Ljubimov's point of view on the character of Lulu; she may be the sweetest, but she's definitely a beast, a less-than-human creature that can be tolerated only when she's caged.

But is she really all that bad? The libretto contains other clues that suggest that Lulu is perhaps more innocent than Ljubimov makes her out to be.

Lulu's background is, of course, mysterious. She appears to be ageless, for one thing; the only character who understands her is Schigolch, a decrepit old man who might have been her lover many, many years ago. And she's chameleon-like; she comfortably wears the guises of mistress, wife and whore, and along with Lulu she goes by the names Eve, Nelly and Mignon.

Yet she speaks the truth - an often painful truth - to her various consorts. And it seems that she speaks the truth to the audience. Berg's music certainly has the ring of sincerity when it supports Lulu's bold declaration of independence in Act II, just before she murders her third husband. The Jacobs translation (''I have not asked in my life to appear in another color than the one which I am known to have. Nor has any man in my life been led to look on me as other than what I am'') is literal but awkward; the Lyric Opera's supertitles, by Francis Rizzo, get the idea across much more succinctly: ''I've never pretended to be anything other than what I am; I'm just what men see in me.''

In the final scene there's another line that, according to the tone of Berg's music, seems utterly sincere. It's sung by Schigolch to Alwa, just after Lulu - now a streetwalker of the sleaziest sort - goes out to find another customer. ''She can't earn a living from love,'' the old man says, ''because her entire life is love itself.''

It makes one wonder. And facts about Berg's life that have been revealed only in the last decade make one wonder all the more.

''Lulu'' is closely based on two plays - ''Earth Spirit'' and ''Pandora's Box'' (actually one big play, but published as two) - by the German writer Benjamin Franklin Wedekind. Because of their allegedly lewd content, the plays were banned when they came out in 1903 and 1904, respectively. It was a private staging of ''Pandora's Box'' that Berg saw in Vienna in 1905. The 20-year-old composer was deeply moved. ''(This) is the really new direction,'' he wrote to a friend. ''The emphasis on the sensual in modern works! . . . at last we have come to the realization that sensuality is not a weakness, does not mean a surrender to one's own will. Rather, it is an immense strength that lies in us - the pivot of all being and thinking.''

Berg seems not to have openly practiced what he preached in that letter. In 1911 he married Helene Nahowski. By 1928, when he first got the idea to make an opera of Wedekind's ''Lulu'' plays, his domestic life appeared to be the very model of non-sensual propriety. Actually, since the spring of 1925 Berg had been having an affair with Hanna Fuchs-Robettin, the sister-in-law of Gustav Mahler's wife Alma. The relationship, according to documents that surfaced only in the mid-1970s, lasted until Berg's death in 1935. It was an intense, though not often consummated, relationship; some Berg scholars believe it was Berg's feelings for Hanna that inspired the hyper-impassioned music of ''Lulu.''

Perhaps that's why Berg's widow so adamantly opposed the completion of Act III.

It could have been done easily enough. Except for a very few passages, Berg had finished all but the orchestration, and in the first several years after Berg's death there was serious talk of Schoenberg, Webern or Zemlinsky doing the job. But nothing came of it, and before long Helene Berg found out not only about her husband's affair but also about an illegitimate daughter he'd fathered when still in his teens.

The world premiere in 1937 involved only the first two acts, then a pantomimed staging of the conclusion of the Wedekind play accompanied by the two relevant movements from Berg's ''Lulu Symphony.'' Helene Berg forbade the planned publication of a piano-vocal score based on the manuscript ''short score.'' She ordered all the ''Lulu'' materials locked in a vault, and it was not until after her death, in 1976, that musicologists officially had access to them.

Between 1937 and 1979, when the Paris Opera presented the work with the third act completed and orchestrated by the Viennese composer Friedrich Cerha, the two-act ''torso'' was all anyone knew of ''Lulu.'' The ''torso'' ends with Lulu asking Alwa, as they start to make love: ''Isn't this the couch on which your father bled to death?'' In the previous scene, before she shoots Alwa's father in the back, Lulu tells Alwa that she'd poisoned his mother. It's not a pretty picture, and from it one could only conclude that Lulu was, indeed, a bad person.

But the third act casts her in a different light. Lulu suffers as she sells her body in order to support Alwa and Schigolch. And Schigolch, who has known her for a long time, says that ''her entire life is love itself.''

What eventually happens to Lulu is horrible. In Ljubimov's staging it is not so easy to feel sorry for her; a mime carries her out of the bedroom where she's been stabbed to death and places her on the bars so that she hangs - like dead meat - when they're raised for the last time. But the music demands sympathy for Lulu, a sympathy that Helene Berg presumably did not want us to feel.