View : 868 Download: 0
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
- 오세진
- Issue Date
- 2018
- Journal Title
- Advances in Mathematics
- ISSN
- 0001-8708
- Citation
- Advances in Mathematics vol. 328, pp. 959 - 1009
- Keywords
- Categorification; Monoidal category; Quantum cluster algebra; Quiver Hecke algebra; Richardson variety
- Publisher
- Academic Press Inc.
- Indexed
- SCIE; 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
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
- Files in This Item:
There are no files associated with this item.
- Export
- RIS (EndNote)
- XLS (Excel)
- XML