论文标题
仿射Q-Schur代数中的细胞
Cells in affine q-Schur algebras
论文作者
论文摘要
我们开发了代数和几何方法，用于针对本文介绍的任意类型的仿射Q-Schur代数的规范基础。建立了仿射Q-Schur代数与相应仿射Hecke代数之间的双重性。我们在仿射Q-Schur代数上引入了一个内部产品，与该代数相对于该代数证明规范的基础是正面的且几乎是正顺序的。然后，我们为仿射Q-Schur代数制定细胞和渐近形式，并开发其基本特性类似于Lusztig建立的仿射Hecke代数的细胞和渐近形式。细胞和渐近代数的结果对于任意有限类型的Q-Schur代数也有效。
We develop algebraic and geometrical approaches toward canonical bases for affine q-Schur algebras of arbitrary type introduced in this paper. A duality between an affine q-Schur algebra and a corresponding affine Hecke algebra is established. We introduce an inner product on the affine q-Schur algebra, with respect to which the canonical basis is shown to be positive and almost orthonormal. We then formulate the cells and asymptotic forms for affine q-Schur algebras, and develop their basic properties analogous to the cells and asymptotic forms for affine Hecke algebras established by Lusztig. The results on cells and asymptotic algebras are also valid for q-Schur algebras of arbitrary finite type.
