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Braid symmetries on bosonic extensions

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arxiv 2408.07312 v1 pith:ZTUC6YIU submitted 2024-08-14 math.RT math.QA

Masaki Kashiwara , Myungho Kim , Se-jin Oh , Euiyong Park This is my paper · ORCID
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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,

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Cited by 1 Pith paper

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  1. Towards Monoidal Categorifications of Twisted Products of Flag Varieties

    math.RT 2026-02 conditional novelty 6.0 of 10

    The Grothendieck ring of the intersection of two monoidal categories C(β)∩C_v contains the cluster algebra of the twisted product of flag varieties, with cluster monomials given by classes of simple objects.

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