# Quantum groups in (1 p) logarithmic conformal field models

#### by Ilya Tipunin

Institution: The University of Melbourne
Date: Tue 5th February 2008
Time: 3:15 PM
Location: Room 213 Richard Berry Building The University of Melbourne

Abstract: The Kazhdan-Lusztig duality for the (1 p) logarithmic conformal field models leads to the equivalence between representation categories of
the chiral algebra of (1 p) model and quantum sl(2) at root of unity.
We consider tensor products of irreducible representations of the quantum sl(2). Then the spaces of multiplicities of projective modules appearing in the tensor product can be identified with coinvariants of the (1 p) model chiral algebra calculated in irreducible representations. This leads to fermionic formulas for the multiplicities and for (1 p) model characters.