Elliptic Algebra U_q,p(g^) and Quantum Z-algebras

2014/04/07 by Farghly, Rasha M., Konno, Hitoshi, Oshima, Kazuyuki
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1404.1738

Abstract

A new definition of the elliptic algebra U_q,p(g^) associated with an untwisted affine Lie algebra g^ is given as a topological algebra over the ring of formal power series in p. We also introduce a quantum dynamical analogue of Lepowsky-Wilson's Z-algebras. The Z-algebra governs the irreducibility of the infinite dimensional U_q,p(g^)-modules. Some level-1 examples indicate a direct connection of the irreducible U_q,p(g^)-modules to those of the W-algebras associated with the coset g^ ⊕ g^ ⊃ (g^)_diag with level (r-g-1,1) (g:the dual Coxeter number), which includes Fateev- Lukyanov's WB_l-algebra.

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