Mirković–Vilonen basis in type 𝐴₁
2021 ◽
Vol 25
(27)
◽
pp. 780-806
Keyword(s):
Let G G be a connected reductive algebraic group over C \mathbb C . Through the geometric Satake equivalence, the fundamental classes of the Mirković–Vilonen cycles define a basis in each tensor product V ( λ 1 ) ⊗ ⋯ ⊗ V ( λ r ) V(\lambda _1)\otimes \cdots \otimes V(\lambda _r) of irreducible representations of G G . We compute this basis in the case G = S L 2 ( C ) G=\mathrm {SL}_2(\mathbb C) and conclude that in this case it coincides with the dual canonical basis at q = 1 q=1 .
1982 ◽
Vol 92
(1)
◽
pp. 65-72
◽
2021 ◽
Vol 25
(37)
◽
pp. 1049-1092
Keyword(s):
2015 ◽
Vol 152
(2)
◽
pp. 299-326
◽
2021 ◽
Vol 25
(21)
◽
pp. 606-643
1971 ◽
Vol 12
(1)
◽
pp. 1-14
◽