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Presenting generalized Schur algebras in types B,C,D
Stephen Doty, Anthony Giaquinto, John Sullivan
We give explicit presentations by generators and relations of certain generalized Schur algebras (associated with tensor powers of the natural representation) in types B, C, D. Thi…
Brauer algebras, symplectic Schur algebras and Schur-Weyl duality
Richard Dipper, Stephen Doty, Jun Hu
In this paper we prove Schur-Weyl duality between the symplectic group and Brauer algebra over an arbitrary infinite field . We show that the natural homomorphism from the Braue…
A generic algebra associated to certain Hecke algebras
Stephen Doty, Karin Erdmann, Anne Henke
We initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain "generic" Hecke algebra, infinite-dimensio…
Decomposition of tensor products of modular irreducibles for $\SL_2$
Stephen Doty, Anne Henke
We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor pr…
Derangements and tensor powers of adjoint modules for sl_n
Georgia Benkart, Stephen Doty
We obtain the decomposition of the tensor space as a module for , find an explicit formula for the multiplicities of its irreducible…
Presenting Schur Algebras
Stephen Doty, Anthony Giaquinto
Motivated by work of R.M. Green, we obtain a presentation of Schur algebras (both the classical and quantized versions) in terms of generators and relations. The presentation is co…