Citation
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/d0bn5e47. https://resolver.caltech.edu/CaltechTHESIS:12082023083025167
Abstract
[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): 

Thesis Committee: 

Defense Date:  27 November 2023 
NonCaltech Author Email:  yuhuijin1995 (AT) gmail.com 
Record Number:  CaltechTHESIS:12082023083025167 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:12082023083025167 
DOI:  10.7907/d0bn5e47 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  16257 
Collection:  CaltechTHESIS 
Deposited By:  Yuhui Jin 
Deposited On:  17 Jan 2024 17:35 
Last Modified:  17 Jan 2024 17:35 
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