arXiv subjects

Tomoyuki Arakawa

Publications and source records attributed to Tomoyuki Arakawa.

59 records · Page 4Linked to original sources

arXiv2005

Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture

We study the representation theory of the superconformal algebra $W_k(g,f_θ)$ associated with a minimal gradation of $g$. Here, $g$ is a simple finite-dimensional Lie superalgebra with a non-degenerate, even supersymmetric invariant bilinear form. Thus, $W_k(g,f_θ)$ can be one of the well-known superconformal algebras including the Virasoro algebra, the Bershadsky-Polyakov algebra, the Neveu-Schwarz algebra, the Bershadsky-Knizhnik algebras, the N=2 superconformal algebra, the N=4 superconformal algebra, the N=3 superconformal algebra and the big N=4 superconformal algebra. We prove the conjecture of V. G. Kac, S.-S. Roan and M. Wakimoto for $W_k(g,f_θ)$. In fact, we show that any irreducible highest weight character of $W_k(g,f_θ)$ at any level $k\in C$ is determined by the corresponding irreducible highest weight character of the Kac-Moody affinization of $g$.

math-ph↗

arXiv2004

Quantized Reductions and Irreducible Representations of W-Algebras

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 representations with non-degenerate highest weights are expressed by Kazhdan-Lusztig polynomials. The irreduciblity conjecture of Frenkel, Kac and Wakimoto is proved completely for the "-" reduction and partially for the "+" reduction. In particular, the existence of the minimal series representations (= the modular invariant representations) of W(g) is proved.

math.QA↗

arXiv2003

Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction

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 consequence, the vanishing conjecture of Frenkel-Kac-Wakimoto is proved for the ``-'' reduction and partially for the ``+'' reduction.

math.QA↗

arXiv1998

Drinfeld Functor and Finite-Dimensional Representations of Yangian

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 polynomials as a consequence.

math.QA↗

arXiv1996

Spectral Decomposition of Path Space in Solvable Lattice Model

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 $\hatsl$ level $l$ integrable modules, which is consistent with the earlier work [1] in the level one case. Also we prove the fermionic character formula of the $\hatsl$ level $l$ integrable representations in consequence.

q-alg↗