On tensor products of irreducible integrable representations

Shifra Reif; R. Venkatesh

doi:10.1016/j.jalgebra.2021.11.007

On tensor products of irreducible integrable representations

Shifra Reif, R. Venkatesh

Department of Mathematics

Indian Institute of Science Bangalore

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider integrable category O representations of Borcherds–Kac–Moody algebras whose Cartan matrix is finite dimensional, and determine the necessary and sufficient conditions for which the tensor product of irreducible representations from this category is isomorphic to another. This result generalizes a fundamental result of C. S. Rajan on unique factorization of tensor products of finite dimensional irreducible representations of finite dimensional simple Lie algebras over complex numbers.

Original language	English
Pages (from-to)	402-423
Number of pages	22
Journal	Journal of Algebra
Volume	592
DOIs	https://doi.org/10.1016/j.jalgebra.2021.11.007
State	Published - 15 Feb 2022

Bibliographical note

Publisher Copyright:
© 2021

Funding

SR was partly funded by ISF Grant No. 1221/17 and ISF Grant No. 1957/21.RV was partially funded by the grants DST/INSPIRE/04/2016/000848, MTR/2017/000347 from DST (Govt. of India), F.510/25/CASII/2018(SAP-I) from UGC (Govt. of India) and an Infosys Young Investigator Award.The authors are thankful to Maria Gorelik for helpful conversations. This research was partially supported by the Minerva Foundation with funding from the Federal German Ministry for Education and Research. The authors are thankful to Maria Gorelik for helpful conversations. This research was partially supported by the Minerva Foundation with funding from the Federal German Ministry for Education and Research.

Funders	Funder number
Federal German Ministry for Education and Research
Minerva Foundation
University Grants Committee
Israel Science Foundation	MTR/2017/000347, F.510/25/CASII/2018, 1221/17, 1957/21, DST/INSPIRE/04/2016/000848

Keywords

Borcherds–Kac–Moody algebras
Integrable representations
Kac–Weyl character formula
Unique factorization

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10.1016/j.jalgebra.2021.11.007

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On tensor products of irreducible integrable representations

Abstract

Bibliographical note

Funding

Keywords

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