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تسجيل مستخدم جديدThe deformed Virasoro algebra at roots of unity
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We discuss some aspects of the representation theory of the deformed Virasoro algebra $virpq$. In particular, we give a proof of the formula for the Kac determinant and then determine the center of $virpq$ for $q$ a primitive N-th root of unity. We derive explicit expressions for the generators of the center in the limit $t=qp^{-1}to infty$ and elucidate the connection to the Hall-Littlewood symmetric functions. Furthermore, we argue that for $q=sqrtN{1}$ 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.
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