Results 1  10
of
227
Branching rules for modular representations of symmetric groups III: Some . . .
 J. LONDON MATH. SOC
, 1996
"... ..."
(Show Context)
The affine permutation groups of rank three
 Proc. London Math. Soc
, 1987
"... Introduction and statement of results Finite primitive permutation groups of rank 3 have been the subject of much study in the past twenty years, leading on the one hand to interesting new groups (for instance, some sporadic groups) and on the other to new techniques in the theory of permutation gro ..."
Abstract

Cited by 40 (2 self)
 Add to MetaCart
Introduction and statement of results Finite primitive permutation groups of rank 3 have been the subject of much study in the past twenty years, leading on the one hand to interesting new groups (for instance, some sporadic groups) and on the other to new techniques in the theory of permutation groups. It is readily seen that if G is a primitive rank 3
POTENTIAL AUTOMORPHY AND CHANGE OF WEIGHT.
"... Abstract. We show that a strongly irreducible, odd, essentially selfdual, regular, weakly compatible system of ladic representations of the absolute Galois group of a totally real field is potentially automorphic. Along the way we prove a new automorphy lifting theorem for ladic representations w ..."
Abstract

Cited by 36 (11 self)
 Add to MetaCart
(Show Context)
Abstract. We show that a strongly irreducible, odd, essentially selfdual, regular, weakly compatible system of ladic representations of the absolute Galois group of a totally real field is potentially automorphic. Along the way we prove a new automorphy lifting theorem for ladic representations where we impose a new condition at l, which we call ‘potential diagonalizability’. This seems to be a more flexible condition than has been previously considered, and allows for substantial ‘change of weight ’ in our automorphy lifting result.
KostkaFoulkes polynomials and Macdonald spherical functions
 in Surveys in Combinatorics 2003, C. Wensley ed., London Math. Soc. Lect. Notes 307 Camb
, 2003
"... Abstract. Generalized HallLittlewood polynomials (Macdonald spherical functions) and generalized KostkaFoulkes polynomials (qweight multiplicities) arise in many places in combinatorics, representation theory, geometry, and mathematical physics. This paper attempts to organize the different defin ..."
Abstract

Cited by 35 (4 self)
 Add to MetaCart
(Show Context)
Abstract. Generalized HallLittlewood polynomials (Macdonald spherical functions) and generalized KostkaFoulkes polynomials (qweight multiplicities) arise in many places in combinatorics, representation theory, geometry, and mathematical physics. This paper attempts to organize the different definitions of these objects and prove the fundamental combinatorial results from “scratch”, in a presentation which, hopefully, will be accessible and useful for both the nonexpert and researchers currently working in this very active field. The combinatorics of the affine Hecke algebra plays a central role. The final section of this paper can be read independently of the rest of the paper. It presents, with proof, Lascoux and Schützenberger’s positive formula for the KostkaFoulkes poynomials in the type A case. The classical theory of HallLittlewood polynomials and the KostkaFoulkes polynomials appears in the monograph of I.G. Macdonald [Mac]. The HallLittlewood polynomials form a basis of the ring of symmetric functions and the KostkaFoulkes polynomials are the entries of the transition matrix between the HallLittlewood polynomials and the Schur functions.
Small degree representations of finite Chevalley groups in defining characteristic
 electronic). MR MR1901354 (2003e:20013
, 2000
"... We determine for all simple simply connected reductive linear algebraic groups defined over a finite field all irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corre ..."
Abstract

Cited by 34 (1 self)
 Add to MetaCart
We determine for all simple simply connected reductive linear algebraic groups defined over a finite field all irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l our bound is proportional to l 3 and for rank 11 much higher. The small rank cases are based on extensive computer calculations.
Nilpotent orbits in good characteristic and the KempfRousseau theory
 J. ALGEBRA
, 2003
"... Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic p> 0, g = LieG, and suppose that p is a good prime for the root system of G. In this paper, we give a fairly short conceptual proof of Pommerening’s theorem [27, 28] which states that any nilpot ..."
Abstract

Cited by 33 (7 self)
 Add to MetaCart
Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic p> 0, g = LieG, and suppose that p is a good prime for the root system of G. In this paper, we give a fairly short conceptual proof of Pommerening’s theorem [27, 28] which states that any nilpotent element in g is Richardson in a distinguished parabolic subalgebra of the Lie algebra of a Levi subgroup of G. As a byproduct, we obtain a short noncomputational proof of the existence theorem for good transverse slices to the nilpotent Gorbits in g (for earlier proofs of this theorem see [15, 36, 24]). We extend recent results of Sommers [35] to reductive Lie algebras of good characteristics thus providing a satisfactory approach to computing the component groups of the centralisers of nilpotent elements in g and unipotent elements in G. Earlier computations of these groups in positive characteristics relied, mostly, on work of Mizuno [20, 21]. Our approach is based on the theory of optimal parabolic subgroups for Gunstable vectors, also known as the Kempf–Rousseau theory, which provides a good substitute for the sl(2)theory prominent in the characteristic zero case.
Generic transfer for general spin groups
 Duke Math. J
"... Abstract. We prove Langlands functoriality for the generic spectrum of general spin groups (both odd and even). Contrary to other recent instances of functoriality, our resulting automorphic representations on the general linear group will not be selfdual. Together with cases of classical groups, t ..."
Abstract

Cited by 32 (10 self)
 Add to MetaCart
Abstract. We prove Langlands functoriality for the generic spectrum of general spin groups (both odd and even). Contrary to other recent instances of functoriality, our resulting automorphic representations on the general linear group will not be selfdual. Together with cases of classical groups, this completes the list of cases of split reductive groups whose Lgroups have classical derived groups. The important transfer from GSp 4 to GL4 follows from our result as a special case. 1.
A new proof of the Mullineux conjecture
 Journal of Algebraic Combinatorics
"... Let Sn be the symmetric group on n letters, k be a field of characteristic p and Dλ be the irreducible kSnmodule corresponding to a pregular partition λ of n, as in [12]. By tensoring Dλ with the 1dimensional sign representation we obtain another irreducible kSnmodule. If p = 0, Dλ ⊗ sgn ∼ = Dλ ..."
Abstract

Cited by 30 (5 self)
 Add to MetaCart
Let Sn be the symmetric group on n letters, k be a field of characteristic p and Dλ be the irreducible kSnmodule corresponding to a pregular partition λ of n, as in [12]. By tensoring Dλ with the 1dimensional sign representation we obtain another irreducible kSnmodule. If p = 0, Dλ ⊗ sgn ∼ = Dλ ′ , where
Schubert cells and cohomology of the space G/P
 31 Fomin S.V. and Kirillov A.N., Quadratic algebras, Dunkl elements, and Schubert calculus, Advances in Geometry, 147182, Progress in Math. 172
, 1973
"... We study the homological properties of the factor space G/P, where G is a complex semisimple Lie group and Ρ a parabolic subgroup of G. To this end we compare two descriptions of the cohomology of such spaces. One of these makes use of the partition of G/P into cells (Schubert cells), while the oth ..."
Abstract

Cited by 30 (0 self)
 Add to MetaCart
(Show Context)
We study the homological properties of the factor space G/P, where G is a complex semisimple Lie group and Ρ a parabolic subgroup of G. To this end we compare two descriptions of the cohomology of such spaces. One of these makes use of the partition of G/P into cells (Schubert cells), while the other consists in identifying the cohomology of G/P with certain polynomials on the Lie algebra of the Cartan subgroup Η of G. The results obtained are used to describe the algebraic action of the Weyl group W of G on the cohomology of G/P. Contents