A Caltech Library Service

On the Hecke Module of GLₙ(k[[z]])\GLₙ(k((z)))/GLₙ(k((z²)))


Jin, Yuhui (2024) On the Hecke Module of GLₙ(k[[z]])\GLₙ(k((z)))/GLₙ(k((z²))). Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/d0bn-5e47.


[See Abstract in text of thesis for correct representation of mathematics]

Every double coset in GLₘ(k[[z]])\GLₘ(k((z)))/GLₘ(k((z²))) is uniquely represented by a block diagonal matrix with diagonal blocks in { 1,z, (11 z \\0 zⁱ \\) (i>1) } if char(k) ≠ 2 and k is a finite field. These cosets form a (spherical) Hecke module H(G,H,K) over the (spherical) Hecke algebra H(G,K) of double cosets in K\G/H, where K=GLₘ(k[[z]]) and H=GLₘ(k((z²))) and G=GLₘ(k((z))). Similarly to Hall polynomial hλ,ν^µ from the Hecke algebra H(G,K), coefficients hλ,ν^µ arise from the Hecke module. We will provide a closed formula for hλ,ν^µ, under some restrictions over λ, ν, µ.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Hecke Module, $\text{GL}_m(k[[z]])\backslash \text{GL}_m(k((z)))/\text{GL}_m(k((z^2)))$, symmetric elliptic difference equation
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Rains, Eric M.
Thesis Committee:
  • Mantovan, Elena (chair)
  • Conlon, David
  • Huang, Jia
  • Rains, Eric M.
Defense Date:27 November 2023
Non-Caltech Author Email:yuhuijin1995 (AT)
Record Number:CaltechTHESIS:12082023-083025167
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16257
Deposited By: Yuhui Jin
Deposited On:17 Jan 2024 17:35
Last Modified:17 Jan 2024 17:35

Thesis Files

[img] PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page