Constructible characters and canonical bases

A 型仿射 Schubert 簇的非交换分解与典范基

Noncommutative resolutions of affine Schubert varieties in type A and canonical bases

针对 GL_n 的仿射 Schubert 簇，构造非交换版本（代数层），导出等价于原分解及其 Steinberg 版本，从而定义反常- exotic t-结构，并证明其 K-理论中不可约对象的类与 Kazhdan-Lusztig 典范基一致。

An Algebraic Characterization of the Affine Canonical Basis

The canonical basis for quantized universal enveloping algebras associated to the finite--dimensional simple Lie algebras, was introduced by Lusztig. The principal technique is the explicit construction (via the braid group action) of a lattice over $\bz[q^{-1}]$. This allows the algebraic characterization of the canonical basis as a certain bar-invariant basis of $\cl$. Here we present a similar algebraic characterization of the affine canonical basis. Our construction is complicated by the need to introduce basis elements to span the ``imaginary'' subalgebra which is fixed by the affine brai…