On the homological construction of the steinberg representation

Khammash, Ahmed A.

doi:10.1016/0022-4049(93)90065-2

Cited by 5 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, we recover a result of Hiss [18] and Khammash [26] in this way. Furthermore, Proposition 3.2 implies that, if q s = 1 for some s ∈ S, then k G is not even a composition factor of St G .…”

Section: The Socle Of the Steinberg Modulesupporting

confidence: 80%

See 1 more Smart Citation

On the $\ell$-modular composition factors of the Steinberg representation

Geck¹

2015

Preprint

View full text Add to dashboard Cite

Let G be a finite group of Lie type and St k be the Steinberg representation of G, defined over a field k. We are interested in the case where k has prime characteristic ℓ and St k is reducible. Tinberg has shown that the socle of St k is always simple. We give a new proof of this result in terms of the Hecke algebra of G with respect to a Borel subgroup and show how to identify the simple socle of St k among the principal series representations of G. Furthermore, we determine the composition length of St k when G = GL n (q) or G is a finite classical group and ℓ is a so-called linear prime.

show abstract

Section: The Socle Of the Steinberg Modulesupporting

confidence: 80%

“…There is only very little general knowledge about the structure of St k in this case. We mention the works of Tinberg [33] (on the socle of St k ), Hiss [18] and Khammash [26] (on trivial composition factors of St k ) and Gow [14] (on the Jantzen filtration of St k ).…”

Section: Introductionmentioning

confidence: 99%

On the $\ell$-modular composition factors of the Steinberg representation

Geck¹

2015

Preprint

View full text Add to dashboard Cite

show abstract

“…Subsequently, Khammash improved this result to show that the socle of I is the trivial KG-module if and only if l divides q + 1, [9]. We will now reprove Khammash's theorem using the methods developed in this paper.…”

Section: Corollarymentioning

confidence: 99%

The Steinberg Lattice of a Finite Chevalley Group and Its Modular Reduction

Gow

2003

J. London Math. Soc.

View full text Add to dashboard Cite

0-Hecke algebra actions on coinvariants and flags

Huang

2013

J Algebr Comb

View full text Add to dashboard Cite

The 0-Hecke algebra Hn(0) is a deformation of the group algebra of the symmetric group Sn. We show that its coinvariant algebra naturally carries the regular representation of Hn(0), giving an analogue of the well-known result for Sn by Chevalley-Shephard-Todd. By investigating the action of Hn(0) on coinvariants and flag varieties, we interpret the generating functions counting the permutations with fixed inverse descent set by their inversion number and major index. We also study the action of Hn(0) on the cohomology rings of the Springer fibers, and similarly interpret the (noncommutative) Hall-Littlewood symmetric functions indexed by hook shapes. P α summed over all compositions α of n, where every P α is a (left) indecomposable H n (0)-module. It follows that {P α : α |= n} is a complete list of non-isomorphic projective indecomposable H n (0)modules, and {C α : α |= n} is a complete list of non-isomorphic simple H n (0)-modules, where C α = top(P α ) = P α / rad P α for all compositions α |= n. for their helpful suggestions and comments.

show abstract

On the homological construction of the steinberg representation

Cited by 5 publications

References 7 publications

On the $\ell$-modular composition factors of the Steinberg representation

On the $\ell$-modular composition factors of the Steinberg representation

The Steinberg Lattice of a Finite Chevalley Group and Its Modular Reduction

0-Hecke algebra actions on coinvariants and flags

Contact Info

Product

Resources

About