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 |
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Pages (from-to) | 402-423 |
Number of pages | 22 |
Journal | Journal of Algebra |
Volume | 592 |
DOIs | |
State | Published - 15 Feb 2022 |
Bibliographical note
Funding Information: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.
Funding Information:
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.
Publisher Copyright:
© 2021
Keywords
- Borcherds–Kac–Moody algebras
- Integrable representations
- Kac–Weyl character formula
- Unique factorization