The based rings of two-sided cells in an affine Weyl group of type $${{\tilde B}_3}$$, I
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DOI: 10.1007/s11425-021-1945-7
Abstract: For type B̃3 we show that Lusztig’s conjecture on the structure of the based ring of two-sided cell corresponding to the unipotent class in Sp6(C) with 3 equal Jordan blocks needs modified. We are concerned… read more here.
Keywords: based ring; affine weyl; two sided; weyl group ... See more keywords
Partial orders on conjugacy classes in the Weyl group and on unipotent conjugacy classes
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DOI: 10.1016/j.aim.2021.107688
Abstract: Let $G$ be a reductive group over an algebraically closed field and let $W$ be its Weyl group. In a series of papers, Lusztig introduced a map from the set $[W]$ of conjugacy classes of… read more here.
Keywords: weyl group; orders conjugacy; partial orders; conjugacy classes ... See more keywords
Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities
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DOI: 10.1016/j.aim.2021.107793
Abstract: We state a conjecture about the Weyl group action coming from Geometric Satake on zero-weight spaces in terms of equivariant multiplicities of Mirkovic-Vilonen cycles. We prove it for small coweights in type A. In this… read more here.
Keywords: group action; vilonen basis; weyl group; equivariant multiplicities ... See more keywords
Action of Weyl group on zero-weight space
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DOI: 10.1016/j.crma.2018.06.005
Abstract: Abstract For any simple complex Lie group, we classify irreducible finite-dimensional representations ρ for which the longest element w 0 of the Weyl group acts non-trivially on the zero-weight space. Among irreducible representations that have… read more here.
Keywords: weyl group; weight; group; zero weight ... See more keywords
The relation ⩽LR on some elements of the affine Weyl group C˜n
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DOI: 10.1016/j.jalgebra.2017.01.024
Abstract: Abstract Let ( W , S ) be the affine Weyl group of type C ˜ n with S its Coxeter generator set. Let Λ ‾ 2 n + 1 be the set of all… read more here.
Keywords: weyl group; relation elements; elements affine; affine weyl ... See more keywords
On the limits of discrete Painlevé equations associated with the affine Weyl group E8
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DOI: 10.1063/1.4978330
Abstract: We study the discrete Painleve equations that can be obtained as limits from the equations associated with the affine Weyl group E8(1). We obtain equations associated with the groups E7(1) and E6(1) as well as… read more here.
Keywords: weyl group; associated affine; equations associated; affine weyl ... See more keywords