A generic multiplication in quantised Schur algebras

Details A generic multiplication in quantised Schur algebras A generic multiplication in quantised Schur algebras

2008-12-03

arxiv.org/abs/0812.0688v1

Mathematics

Quantum Algebra

Scientific paper

We define a generic multiplication in quantised Schur algebras and thus obtain a new algebra structure in the Schur algebras. We prove that via a modified version of the map from quantum groups to quantised Schur algebras, defined by A. A. Beilinson, G. Lusztig and R. MacPherson, a subalgebra of this new algebra is a quotient of the monoid algebra in Hall algebras studied by M. Reineke. We also prove that the subalgebra of the new algebra gives a geometric realisation of a positive part of 0-Schur algebras. Consequently, we obtain a multiplicative basis for the positive part of 0-Schur algebras.

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