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Kus, Deniz and Littelmann, Peter (2015). FUSION PRODUCTS AND TOROIDAL ALGEBRAS. Pac. J. Math., 278 (2). S. 427 - 446. BERKELEY: PACIFIC JOURNAL MATHEMATICS. ISSN 0030-8730

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Abstract

We study the category of finite-dimensional bigraded representations of toroidal current algebras associated to finite-dimensional complex simple Lie algebras. Using the theory of graded representations for current algebras, we construct in different ways objects in that category and prove them to be isomorphic. As a consequence we obtain generators and relations for certain types of fusion products, including the N-fold fusion product of V (lambda). This result shows that the fusion product of these types is independent of the chosen parameters, proving a special case of a conjecture by Feigin and Loktev. Moreover, we prove a conjecture by Chari, Fourier and Sagaki on truncated Weyl modules for certain classes of dominant integral weights and show that they are realizable as fusion products. In the last section we consider the case g = sl(2) and compute a PBW type basis for truncated Weyl modules of the associated current algebra.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kus, Deniz UNSPECIFIED UNSPECIFIED UNSPECIFIED Littelmann, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-385468
DOI:	10.2140/pjm.2015.278.427
Journal or Publication Title:	Pac. J. Math.
Volume:	278
Number:	2
Page Range:	S. 427 - 446
Date:	2015
Publisher:	PACIFIC JOURNAL MATHEMATICS
Place of Publication:	BERKELEY
ISSN:	0030-8730
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DEMAZURE MODULES; WEYL MODULES; LIMIT CONSTRUCTIONS; TENSOR-PRODUCTS; CRYSTALS; FORMULAS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/38546