5,794 research outputs found
On the endomorphisms of Weyl modules over affine Kac-Moody algebras at the critical level
We present an independent short proof of the main result of arXiv:0706.3725
that the algebra of endomorphisms of a Weyl module of critical level is
isomorphic to the algebra of functions on the space of monodromy-free opers on
the disc with regular singularity and residue determined by the highest weight
of the Weyl module. We derive this from the results of arXiv:0712.1183 about
the shift of argument subalgebras.Comment: 9 page
Comments on the Deformed W_N Algebra
We obtain an explicit expression for the defining relation of the deformed
W_N algebra, DWA(^sl_N)_{q,t}. Using this expression we can show that, in the
q-->1 limit, DWA(^sl_N)_{q,t} with t=e^{-2\pi i/N}q^{(k+N)/N} reduces to the
sl_N-version of the Lepowsky-Wilson's Z-algebra of level k, ZA(^sl_N)_k. In
other words DWA(^sl_N)_{q,t} with t=e^{-2\pi i/N}q^{(k+N)/N} can be considered
as a q-deformation of ZA(^sl_N)_k. In the appendix given by H.Awata, S.Odake
and J.Shiraishi, we present an interesting relation between DWA(^sl_N)_{q,t}
and \zeta-function regularization.Comment: 10 pages, LaTeX2e with ws-ijmpb.cls, Talk at the APCTP-Nankai Joint
Symposium on ``Lattice Statistics and Mathematical Physics'', 8-10 October
2001, Tianjin Chin
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