A Generic Multiplication in Quantised Schur Algebras
نویسنده
چکیده
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 in [1], a subalgebra of this new algebra is a quotient of the monoid algebra in Hall algebras studied in [10]. We also prove that the subalgebra of the new algebra gives a geometric realisation of a positive part of 0-Schur algebras, defined in [4]. Consequently, we obtain a multiplicative basis for the positive part of 0-Schur algebras.
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