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Monoidal categories associated with strata of flag manifolds

Title
Monoidal categories associated with strata of flag manifolds
Authors
Kashiwara M.Kim M.Oh S.-J.Park E.
Ewha Authors
오세진
SCOPUS Author ID
오세진scopus
Issue Date
2018
Journal Title
Advances in Mathematics
ISSN
0001-8708JCR Link
Citation
Advances in Mathematics vol. 328, pp. 959 - 1009
Keywords
CategorificationMonoidal categoryQuantum cluster algebraQuiver Hecke algebraRichardson variety
Publisher
Academic Press Inc.
Indexed
SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
We construct a monoidal category Cw,v which categorifies the doubly-invariant algebra CN′(w)[N]N(v) associated with Weyl group elements w and v. It gives, after a localization, the coordinate algebra C[Rw,v] of the open Richardson variety associated with w and v. The category Cw,v is realized as a subcategory of the graded module category of a quiver Hecke algebra R. When v=id, Cw,v is the same as the monoidal category which provides a monoidal categorification of the quantum unipotent coordinate algebra Aq(n(w))Z[q,q−1] given by Kang–Kashiwara–Kim–Oh. We show that the category Cw,v contains special determinantial modules M(w≤kΛ,v≤kΛ) for k=1,…,ℓ(w), which commute with each other. When the quiver Hecke algebra R is symmetric, we find a formula of the degree of R-matrices between the determinantial modules M(w≤kΛ,v≤kΛ). When it is of finite ADE type, we further prove that there is an equivalence of categories between Cw,v and Cu for w,u,v∈W with w=vu and ℓ(w)=ℓ(v)+ℓ(u). © 2018 Elsevier Inc.
DOI
10.1016/j.aim.2018.02.013
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자연과학대학 > 수학전공 > Journal papers
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