Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 047, 20 pages      arXiv:1310.5321      https://doi.org/10.3842/SIGMA.2014.047
Contribution to the Special Issue on New Directions in Lie Theory

Graded Limits of Minimal Affinizations in Type D

Katsuyuki Naoi
Institute of Engineering, Tokyo University of Agriculture and Technology, 3-8-1 Harumi-cho, Fuchu-shi, Tokyo, Japan

Received October 30, 2013, in final form April 14, 2014; Published online April 20, 2014

Abstract
We study the graded limits of minimal affinizations over a quantum loop algebra of type D in the regular case. We show that the graded limits are isomorphic to multiple generalizations of Demazure modules, and also give their defining relations. As a corollary we obtain a character formula for the minimal affinizations in terms of Demazure operators, and a multiplicity formula for a special class of the minimal affinizations.

Key words: minimal affinizations; quantum affine algebras; current algebras.

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