Physics – High Energy Physics – High Energy Physics - Theory

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1997-10-22

Commun. Math. Phys. 196 (1998) 249-288

Physics

High Energy Physics

High Energy Physics - Theory

51 pages, TeX (with amssym.def)

Scientific paper

10.1007/s002200050421

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.

**Bouwknegt Peter**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

**Pilch Krzysztof**

Physics – High Energy Physics – High Energy Physics - Theory

Scientist

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