量子化Schur代数中的一般乘法
A generic multiplication in quantised Schur algebras
摘要：
在量子化Schur代数中定义了一个通有乘法，从而得到了量子化Schur代数中一个新的代数结构。我们证明，通过一个修改的版本的映射，从量子群量子Schur代数，定义的A。A. Beilinson，G. Lusztig和R. MacPherson，这个新代数的子代数是M. Reineke.我们还证明了新代数的子代数给出了0-Schur代数的正部分的几何实现。从而得到了0-Schur代数的正部分的乘法基。
英文摘要：
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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