Representation ring of Levi subgroups versus cohomology ring of flag varieties II

JOURNAL OF ALGEBRA

卷:556

Article

Kumar, Shrawan¹  Rogers, Sean¹ 

[1] Univ N Carolina, Dept Math, Chapel Hill, NC 27599 USA

关键词: Cohomology;    Levi subgroups;    Isotropic Grassmannians;    Representation ring;   

DOI  :  10.1016/j.jalgebra.2020.02.029

来源: Elsevier

【 摘 要 】

For any reductive group G and a parabolic subgroup P with its Levi subgroup L, the first author in [5] introduced a ring homomorphism xi(p)(lambda) : Rep(lambda-poly)(C) (L) -> H*(G/P,C), where Rep(lambda-poly)(C) (L) is a certain subring of the complexified representation ring of L (depending upon the choice of an irreducible representation V(lambda) of G with highest weight lambda). In this paper we study this homomorphism for G = Sp(2n) and its maximal parabolic subgroups Pn-k for any 1 <= k <= n - 1 (with the choice of V(lambda) to be the defining representation V(w(1)) in C-2n). Thus, we obtain a C-algebra homomorphism xi(n,k) : Rep(w1-poly)(Sp(2k)) H* (IG(n- k, 2n), C). Our main result asserts that xi(n,)(k) is injective when n tends to infinity keeping k fixed. Similar results are obtained for the odd orthogonal groups. Published by Elsevier Inc.

【 授权许可】

Free