Universität zu Köln

Kus, Deniz (2018). Representations of Lie uperalgebras S with Fusion Flags. Int. Math. Res. Notices, 2018 (17). S. 5455 - 5486. OXFORD: OXFORD UNIV PRESS. ISSN 1687-0247

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Abstract

We study the category of finite-dimensional representations for a basic classical Lie superalgebra g = g0 circle plus g1. For the ortho-symplectic Lie superalgebra g = osp(1, 2n), we show that various objects in that category admit a fusion flag, that is, a sequence of graded g(0)[t]-modules such that the successive quotients are isomorphic to fusion products. Among these objects we find fusion products of finite-dimensional irreducible g-modules, truncated Weyl modules and Demazure type modules. This result shows that the character of these types of representations can be expressed in terms of characters of fusion products and we prove that the graded multiplicities are given by products of q-binomial coefficents. Moreover, we establish a presentation for these types of fusion products in terms of generators and relations of the enveloping algebra.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kus, Deniz UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-174057
DOI:	10.1093/imrn/rnx058
Journal or Publication Title:	Int. Math. Res. Notices
Volume:	2018
Number:	17
Page Range:	S. 5455 - 5486
Date:	2018
Publisher:	OXFORD UNIV PRESS
Place of Publication:	OXFORD
ISSN:	1687-0247
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DEMAZURE MODULES; WEYL MODULES; TENSOR-PRODUCTS; CRYSTALS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/17405