Hook Modules for General Linear Groups
نویسنده
چکیده
For an arbitrary infinite field k of characteristic p > 0, we completely describe the structure of a block of the algebraic monoid Mn(k) (all n×n matrices over k), or, equivalently, a block of the Schur algebra S(n, p), whose simple modules are indexed by p-hook partitions. This leads to a character formula for certain simple GLn(k)-modules, valid for all n and all p.
منابع مشابه
A Multivariate “inv” Hook Formula for Forests
Björner and Wachs provided two q-generalizations of Knuth’s hook formula counting linear extensions of forests: one involving the major index statistic, and one involving the inversion number statistic. We prove a multivariate generalization of their inversion number result, motivated by specializations related to the modular invariant theory of finite general linear groups.
متن کامل‘SOME REMARKS ON GILL’S THEOREMS ON YOUNG MODULES’ AUTHOR(S): Professor Stephen Donkin Some remarks on Gill’s Theorems on Young Modules
In a recent paper, [2], Gill, using methods of the modular representation theory of finite groups, describes some results on the tensor product of Young modules for symmetric groups. We here give an alternative approach using the polynomial representation theory of general linear groups and the Schur functor. The main result is a formula for the multiplicities of Young modules in a tensor produ...
متن کاملThe Prevalence of Unanticipated Hamate Hook Abnormalities in Computed Tomography Scans: A Retrospective Study
Background:It is possible that some hamate hook fractures are not diagnosed or treated, thereby affecting the study of their natural history. Study of the prevalence of incidental hamate hook fractures, nonunions, and other abnormalities on computed tomography (CT) ordered for another reason could document a subset of undiagnosed and untreated hamate hook fractures which might change our under...
متن کاملGeneralized Hook Lengths in Symbols and Partitions
In this paper we present, for any integer d, a description of the set of hooks in a d-symbol. We then introduce generalized hook length functions for a d-symbol, and prove a general result about them, involving the core and quotient of the symbol. We list some applications, for example to the well-known hook lengths in integer partitions. This leads in particular to a generalization of a relati...
متن کاملThe Combinatorics of the Garsia-Haiman Modules for Hook Shapes
Several bases of the Garsia-Haiman modules for hook shapes are given, as well as combinatorial decomposition rules for these modules. These bases and rules extend the classical ones for the coinvariant algebra of type A. We also give a decomposition of the Garsia-Haiman modules into descent representations.
متن کامل