Longest Weyl group elements in action. (English) Zbl 1523.20066
Greenstein, Jacob (ed.) et al., Interactions of quantum affine algebras with cluster algebras, current algebras and categorification. In honor of Vyjayanthi Chari on the occasion of her 60th birthday. Based on the summer school and the conference, Washington, DC, USA, June 2018. Cham: Birkhäuser. Prog. Math. 337, 245-276 (2021).
Summary: Inspired from graded quiver varieties, we attach a Weyl-like group \(W^{\langle n \rangle}\) to a Cartan matrix and a nonnegative integer \(n\). As the integer varies, we get a projective system. In type \(A_\ell\), the group \(W^{\langle n \rangle}\) is related to reduced Burau representations, and in general to complex reflection groups. Behavior of the longest Weyl group elements in \(W^{\langle n \rangle}\) is studied in detail. The results will be used in the analysis by Li (in preparation) of graded/cyclic quiver varieties in the spirit of [the first author, Represent. Theory 23, 1–56 (2019; Zbl 1403.16009)].
For the entire collection see [Zbl 1481.17001].
For the entire collection see [Zbl 1481.17001].
MSC:
| 20F55 | Reflection and Coxeter groups (group-theoretic aspects) |
| 16G20 | Representations of quivers and partially ordered sets |
Citations:
Zbl 1403.16009References:
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