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1
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Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians

100%
Lakshmibai V., Raghavan K., Sankaran P.
Open Mathematics
|
2009
|
tom 7
|
nr 2
214-223
EN
It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.
2
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Normalizers and self-normalizing subgroups II

76%
Širola B.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1317-1332
EN
Let $\mathbb{K}$ be a field, G a reductive algebraic $\mathbb{K}$-group, and G 1 ≤ G a reductive subgroup. For G 1 ≤ G, the corresponding groups of $\mathbb{K}$-points, we study the normalizer N = N G(G 1). In particular, for a standard embedding of the odd orthogonal group G 1 = SO(m, $\mathbb{K}$) in G = SL(m, $\mathbb{K}$) we have N ≅ G 1 ⋊ µm($\mathbb{K}$), the semidirect product of G 1 by the group of m-th roots of unity in $\mathbb{K}$. The normalizers of the even orthogonal and symplectic subgroup of SL(2n, $\mathbb{K}$) were computed in [Širola B., Normalizers and self-normalizing subgroups, Glas. Mat. Ser. III (in press)], leaving the proof in the odd orthogonal case to be completed here. Also, for G = GL(m, $\mathbb{K}$) and G 1 = O(m, $\mathbb{K}$) we have N ≅ G 1 ⋊ $\mathbb{K}$ ×. In both of these cases, N is a self-normalizing subgroup of G.
3
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Twisted gamma filtration and algebras with orthogonal involution

64%
Junkins C.
Open Mathematics
|
2014
|
tom 12
|
nr 3
421-428
EN
For the Grothendieck group of a split simple linear algebraic group, the twisted γ-filtration provides a useful tool for constructing torsion elements in -rings of twisted flag varieties. In this paper, we construct a non-trivial torsion element in the γ-ring of a complete flag variety twisted by means of a PGO-torsor. This generalizes the construction in the HSpin case previously obtained by Zainoulline.
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