The Deformed Virasoro Algebra at Roots of Unity
Abstract
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 Virp,q for $q$ a primitive Nth root of unity. We derive explicit expressions for the generators of the center in the limit t=qp-1→∞ and elucidate the connection to the Hall-Littlewood symmetric functions. Furthermore, we argue that for 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.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- August 1998
- DOI:
- 10.1007/s002200050421
- arXiv:
- arXiv:q-alg/9710026
- Bibcode:
- 1998CMaPh.196..249B
- Keywords:
-
- Explicit Expression;
- Representation Theory;
- Symmetric Function;
- Virasoro Algebra;
- Gentile Statistic;
- Mathematics - Quantum Algebra;
- High Energy Physics - Theory
- E-Print:
- 51 pages, TeX (with amssym.def)