Codimensions of root valuation strata

Generalized affine Springer fibers

This paper studies two new kinds of affine Springer fibers that are adapted to the root valuation strata of Goresky-Kottwitz-MacPherson. In addition it develops various linear versions of Katz's Hodge-Newton decomposition.

扩展仿射Weyl群判别层的斋藤行列式

The Saito determinant for extended affine Weyl discriminant strata

该研究计算扩展仿射Weyl群判别层的斋藤行列式，将Weyl分母公式因式分解推广到更高余维数层，得到Antoniou-Feigin-Strachan结果的q-模拟细化。

Affine hyperplane arrangements and Jordan classes

We study the geometry of the stratification induced by an affine hyperplane arrangement H on the quotient of a complex affine space by the action of a discrete group preserving H. We give conditions ensuring normality or normality in codimension 1 of strata. As an application, we provide the list of those categorical quotients of closures of Jordan classes and of sheets in all complex simple algebraic groups that are normal. In the simply connected case, we show that normality of such a quotient is equivalent to its smoothness.