Arakawa, Tomoyuki, Fiebig, Peter
We study the restricted category O for an affine Kac--Moody algebra at the critical level. In particular, we prove the first part of the Feigin-Frenkel conjecture: the linkage principle for...
On the restricted Verma modules at the critical level (2008)
Arakawa, Tomoyuki, Fiebig, Peter
We study the restricted Verma modules of an affine Kac-Moody algebra at the critical level with special emphasis on their Jordan-H"older multiplicities. The Feigin-Frenkel conjecture gives a formula...
Arakawa, Tomoyuki, Chebotarov, Dmytro, Malikov, Fyodor
We propose a notion of algebra of {\it twisted} chiral differential operators over algebraic manifolds with vanishing 1st Pontrjagin class. We show that such algebras possess families of modules...
Representation theory of W-algebras, II: Ramond twisted representations (2008)
We study the Ramond twisted representations of the affine W-algebra W^k(g,f) in the case that f admits a good even grading. We establish the vanishing and the almost irreducibility of the...
Characters of representations of affine Kac-Moody Lie algebras at the critical level (2007)
We present an explicit character formula for the irreducible highest weight representations of the non-twisted affine Kac-Moody Lie algebra at the critical level which are integrable over the...
A new proof of the Kac-Kazhdan conjecture (2006)
We give a new proof of the Kac-Kazhdan character formula. We show that it easily follows from the general result on the quantized Drinfeld-Sokolov reduction previously obtained by the author.
Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture (2005)
We study the representation theory of the superconformal algebra $\mathcal{W}_k(\mathfrak{g},f_{\theta})$ associated with a minimal gradation of $\frak{g}$. Here, $\frak{g}$ is a simple...
Representation Theory of W-Algebras (2005)
This paper is the detailed version of math.QA/0403477 (T. Arakawa, Quantized Reductions and Irreducible Representations of W-Algebras) with extended results; We study the representation theory of the...
Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture (2004)
We study the representation theory of the superconformal algebra $W_k(g,f_{\theta})$ associated with a minimal gradation of $g$. Here, $g$ is a simple finite-dimensional Lie superalgebra with a...
Quantized Reductions and Irreducible Representations of W-Algebras (2004)
We study the representations of the W-algebra W(g) associated to an arbitrary finite-dimensional simple Lie algebra g via the quantized Drinfeld-Sokolov reductions. The characters of irreducible...
Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction (2004)
We prove a vanishing theorem of the cohomology arising from the two quantized Drinfeld-Sokolov reductions (“+” and “−” reductions) introduced by Fe&Ibreve;gin and Frenkel, and by Frenkel,...
Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction (2003)
We prove a vanishing theorem of the cohomology arising from the two Quantized Drinfeld-Sokolov reductions (``+'' and ``-'' reduction) introduced by Feigin-Frenkel and Frenkel-Kac-Wakimoto. As a...
Drinfeld Functor and Finite-Dimensional Representations of Yangian (1998)
We extend the results of Drinfeld on Drinfeld functor to the case l>n. We present the character of finite-dimensional representations of the Yangian Y(sl_n) in terms of the Kazhdan-Lusztig...
Spectral decomposition of path space in solvable lattice model (1996)
Arakawa, Tomoyuki, Nakanishi, Tomoki, Oshima, Kazuyuki, Tsuchiya, Akihiro
Spectral Decomposition of Path Space in Solvable Lattice Model (1995)
Arakawa, Tomoyuki, Nakanishi, Tomoki, Oshima, Kazuyuki, Tsuchiya, Akihiro
We give the {\it spectral decomposition} of the path space of the $U_q(\hatsl)$ vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the...