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SUMMARY:Edmund Karasiewicz (Ben-Gurion University)
DTSTART:20210201T180000Z
DTEND:20210201T183000Z
DTSTAMP:20260423T021221Z
UID:POINT/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/25/">T
 he Twisted Satake Transform and the Casselman-Shalika Formula</a>\nby Edmu
 nd Karasiewicz (Ben-Gurion University) as part of POINT: New Developments 
 in Number Theory\n\n\nAbstract\nThe Fourier coefficients of automorphic fo
 rms are an important object of study due to their connection to $L$-functi
 ons. In the adelic framework\, constructions of $L$-functions involving Fo
 urier coefficients (e.g. Langland-Shahidi and Rankin-Selberg methods) natu
 rally lead to spherical Whittaker functions on $p$-adic groups. Thus we wo
 uld like to understand these spherical Whittaker functions to better under
 stand $L$-functions.\n\nCasselman-Shalika determined a formula for the sph
 erical Whittaker functions\, and basic algebraic manipulations reveal that
  their formula can be more succinctly expressed in terms of characters of 
 the Langlands dual group. We will describe a new proof of the Casselman-Sh
 alika formula that provides a conceptual explanation of the appearance of 
 characters.\n
LOCATION:https://researchseminars.org/talk/POINT/25/
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