Just to expand a little bit on @Paulie_D's quotation
According to the author, Aslan is not an allegorical portrayal of Christ, but rather a suppositional incarnation of Christ Himself
Serendipitously, I was just reading John Granger's The Hidden Key to Harry Potter (spoiler alert: it's no coincidence that his name rhymes with "heir of the Pater"), which strenuously asserts the difference between childish allegory and true symbolism. Granger writes:
As one of C.S. Lewis' Oxford students reminds us, "attaching to the symbol for its own sake apart from its higher meaning," the mistake of the materialists, separates man from the greater, transcendent life for which he is designed [...] (Martin Lings, Symbol and Archetype, p. 4).
Please note that symbolists are not writing "allegories." Allegories are story-puzzles that are often just ironic or satirical retellings of other stories, sometimes historical, sometimes "spiritual," but all are about our world and its realities as we experience it. Tolkien, a symbolist extraordinaire, resisted every attempt to categorize The Lord of the Rings as an allegory with tremendous verbal violence; he felt there could be no greater misunderstanding of what he was doing than to explain it as an allegory of the second world war or some other event. If anything, the second world war was a symbol of the eternal conflicts and verities The Lord of the Rings illumined. The same can be said of Lewis' fiction and Rowling's; this is writing of a different kind than the allegorical Gulliver's Travels, or even Pilgrim's Progress. (For Lewis' careful distinction between "Allegory, Supposal, and Symbolism," especially as it applies to his Chronicles of Narnia, see Walter Hooper's C.S. Lewis: Companion & Guide, pp. 423–429.)
In this "symbolist" worldview, a symbol (such as Aslan's appearance as a lion) is not a mere rebus ("Aha, the lion stands for Jesus!"), but rather a "window" through which we glimpse the higher reality — concepts such as power, majesty, loyalty, empathy, self-sacrifice, redemption.
So when Aslan says "In your world, I have another name," he doesn't mean that he "secretly is" or "represents" some person from our world; this isn't "Guess Who?" or Rumpelstiltskin. Aslan embodies and symbolizes higher realities that are symbolized in our world as well — just as they are symbolized in every world.
So, yes, absolutely, Aslan is Jesus Christ (especially bearing in mind that Lewis was a devout Christian, and bearing in mind that Lewis said so :)). But it's not a simple matter of the two being equivalent, or one allegorically "representing" the other. For example, if Lewis had meant to write a strict allegory, we could fault him for how the Aslan story mixes up bits of Jesus's sacrifice with bits of Samson's hair-shearing. As an allegory, the details are all wrong. But as symbolism, we know that Jesus and Samson both act as windows onto a higher reality through which we glimpse eternal truths — majesty, betrayal, sorrow, self-sacrifice — and Aslan does too.