The Deformed Virasoro Algebra at Roots of Unity
نویسنده
چکیده
We discuss some aspects of the representation theory of the deformed Virasoro algebra Virp,q. In particular, we give a proof of the formula for the Kac determinant and then determine the center of Virp,q for q a primitive N -th root of unity. We derive explicit expressions for the generators of the center in the limit t = qp → ∞ and elucidate the connection to the Hall-Littlewood symmetric functions. Furthermore, we argue that for q = N √ 1 the algebra describes ‘Gentile statistics’ of order N − 1, i.e., a situation in which at most N − 1 particles can occupy the same state. ADP-97-22/M53 USC-97/17 q-alg/9710026 October 1997
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