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.
On the Cohomological Hall Algebra of Dynkin quivers
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abstract
Consider the Cohomological Hall Algebra as defined by Kontsevich and Soibelman, associated with a Dynkin quiver. We reinterpret the geometry behind the multiplication map in the COHA, and give an iterated residue formula for it. We show natural subalgebras whose product is the whole COHA (except in the $E_8$ case). The dimension count version of this statement is an identity for quantum dilogarithm series, first proved by Reineke. We also show that natural structure constants of the COHA are universal polynomials representing degeneracy loci, a.k.a. quiver polynomials.
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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.