ABSTRACT.
I will introduce a new method, using smoothening of a certain scheme over DVR, to study stable orbital integrals for regular semisimple elements and for the unit element of the Hecke algebras in classical Lie algebras gl_n, u_n, sp_2n. As a byproduct, I will explain closed formulas for orbital integrals associated with an arbitrary element of the Hecke algebra in gl_3, and lower bounds/conjectures to estimate values of stable orbital integrals for the other cases. This is based on joint works with Taeyeoup Kang and/or Yuchan Lee.
CMC Algebra Seminar