Braid symmetries on bosonic extensions
Representation Theory
2024-08-15 v1 Quantum Algebra
Abstract
We introduce a family of automorphisms on the bosonic extension of arbitrary type and show that they satisfy the braid relations. They preserve the global basis and the crystal basis. Using this braid group action, we define a subalgebra for each positive braid word, which possesses the PBW type basis. As an application, we show that the tensor product decomposition of the positive bosonic extionsion,
Cite
@article{arxiv.2408.07312,
title = {Braid symmetries on bosonic extensions},
author = {Masaki Kashiwara and Myungho Kim and Se-jin Oh and Euiyong Park},
journal= {arXiv preprint arXiv:2408.07312},
year = {2024}
}
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38 pages