Difference between revisions of "NTS ABSTRACTSpring2021"

From UW-Math Wiki
Jump to: navigation, search
(Created page with "Return to [https://www.math.wisc.edu/wiki/index.php/NTS ] == Jan 28 == <center> {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspa...")
Line 1: Line 1:
Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]
Return to [https://www.math.wisc.edu/wiki/index.php/NTS Main Page]

Revision as of 19:25, 11 January 2021

Return to Main Page

Jan 28

Monica Nevins
Interpreting the local character expansion of p-adic SL(2)

The Harish-Chandra—Howe local character expansion expresses the character of an admissible representation of a p-adic group G as a linear combination with complex coefficients of the (finitely many!) Fourier transforms of nilpotent orbital integrals \(\widehat{\mu}_{\mathcal{O}}\) --- near the identity. Approaching from another direction: we can restrict the representation to any compact open subgroup K of G, obtaining its branching rules, which also describe the representation near the identity, in a different sense. We show that for G=SL(2,k), k a nonarchimedean local field, where the branching rules to maximal compact open subgroups K are known, each of these terms \(\widehat{\mu}_{\mathcal{O}}\) can be interpreted as the character \(\tau_{\mathcal{O}}\) of a representation of K, up to an error term arising from the zero orbit. Moreover, the irreducible components of \(\tau_{\mathcal{O}}\) are explicitly constructed from the K -orbits in \(\mathcal{O}\). This work in progress offers a conjectural alternative interpretation of branching rules of admissible representations.