Dimensions of Affine Springer Fibers for Some ${\mathrm{GL}}_n$ Symmetric Spaces

Abstract

We determine a formula for the dimension of a family of affine Springer fibers associated to a symmetric space arising from the block diagonal embedding ${\mathrm{GL}}_n\times {\mathrm{GL}}_n\hookrightarrow {\mathrm{GL}}_{2n}$ . As an application, we determine the dimension of affine Springer fibers attached to certain unitary symmetric spaces.

arXiv comment9 pages, comments and suggestions welcome