# A generic multiplication in quantized Schur algebras

### Reference:

Su, X., 2010. A generic multiplication in quantized Schur algebras. *The Quarterly Journal of Mathematics*, 61 (4), pp. 497-510.

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### Official URL:

http://dx.doi.org/10.1093/qmath/hap016

### Abstract

We define a generic multiplication in quantized 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 quantized Schur algebras, defined in (A. A. Beilinson, G. Lusztig and R. MacPherson, A geometric setting for the quantum deformation of GL(n), Duke Math. J. 61 (1990), 655-677), a subalgebra of this new algebra is a quotient of the monoid algebra in Hall algebras studied in (M. Reineke, Generic extensions and multiplicative bases of quantum groups at q = 0, Represent. Theory 5 (2001), 147-163). We also prove that the subalgebra of the new algebra gives a geometric realization of a positive part of 0-Schur algebras, defined in (S. Donkin, The q-Schur Algebra, London Mathematical Society Lecture Note Series 253. Cambridge University Press, Cambridge, 1998, x + 179. ISBN: 0-521-64558-1.). Consequently, we obtain a multiplicative basis for the positive part of 0-Schur algebras.

### Details

Item Type | Articles |

Creators | Su, X. |

DOI | 10.1093/qmath/hap016 |

Departments | Faculty of Science > Mathematical Sciences |

Refereed | No |

Status | Published |

ID Code | 22188 |

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