Support varieties of line bundle cohomology groups for SL3(k)

JOURNAL OF ALGEBRA

卷:448

Article

Hardesty, William D.¹ 

[1] Univ Georgia, Dept Math, Athens, GA 30602 USA

关键词: Support varieties;    Sheaf cohomology;    SL3;    A(2);    Character formulas;    Generic dimension;    Quantum dimension;   

DOI  :  10.1016/j.jalgebra.2015.09.034

来源: Elsevier

【 摘 要 】

Let G = SL3(k) where k is a field of characteristic p > 0 and let lambda is an element of X(T) be any weight with corresponding line bundle L(lambda) on G/B. In this paper we compute the support varieties for all modules of the form H-i(lambda) := H-i(G/B,L(lambda)) over the first Frobenius kernel G(1). The calculation involves certain recursive character formulas given by Donkin (cf. [51) which can be used to compute the characters of the line bundle cohomology groups. In the case where lambda is a p -regular weight and M = H-i(lambda) not equal 0 for some i, these formulas are used to show that any pth root of unity zeta is not a root of the generic dimension of M. To handle the case where lambda is not p -regular, we employ techniques similar to those used by Drupieski, Nakano and Parshall (cf. (1) to show that the module H-i(lambda) is not projective over G(1) whenever it is nonzero and lambda lies outside of the Steinberg block. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free