Quiver Schur algebras are realized as operator algebras on cohomological Hall algebras, with shuffle descriptions reinterpreted using Demazure operators, plus results on mixed versions and geometric realizations of modified algebras.
Generalized quiver Hecke algebras
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abstract
We generalize the geometric construction of quiver Hecke algebras from Varagnolo and Vasserot to a setup with arbitrary connected reductive groups. This corresponds to replacing quiver representations by generalized quiver representations introduced by Derksen and Weyman. The class of algebras which we construct contains (affine) nil Hecke algebras, skew group rings of Weyl groups with polynomial rings and quiver Hecke algebras. We describe an explicit faithful representation in a polynomial ring and we calculate the generators and relations for these algebras.
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math.RT 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Quiver Schur algebras and cohomological Hall algebras
Quiver Schur algebras are realized as operator algebras on cohomological Hall algebras, with shuffle descriptions reinterpreted using Demazure operators, plus results on mixed versions and geometric realizations of modified algebras.