Integration on $p$-adic groups and crystal bases
نویسندگان
چکیده
منابع مشابه
INTEGRATION ON p-ADIC GROUPS AND CRYSTAL BASES
Let G = GLr+1 over a nonarchimedean local field F . The Kashiwara crystal B(∞) is the quantized enveloping algebra of the lower triangular maximal unipotent subgroup N−. Examples are given where an integral over N−(F ) may be replaced by a sum over B(∞). Thus the Gindikin-Karpelevich formula evaluates the integral of the standard spherical vector in the induced model of a principal series repre...
متن کاملRepresentation theory of p-adic groups and canonical bases
In this paper, we interpret the Gindikin–Karpelevich formula and the Casselman–Shalika formula as sums over Kashiwara–Lusztig’s canonical bases, generalizing the results of Bump and Nakasuji (2010) [7] to arbitrary split reductive groups. We also rewrite formulas for spherical vectors and zonal spherical functions in terms of canonical bases. In a subsequent paper Kim and Lee (preprint) [14], w...
متن کاملON p-ADIC FUNCTIONAL INTEGRATION
p-Adic generalization of the Feynman path integrals in quantum mechanics is considered. The probability amplitude Kv(x, t′′; x′, t′) (v = ∞, 2, 3, · · · , p, · · ·) for a particle in a constant field is calculated. Path integrals over Qp have the same form as those over R.
متن کاملp-adic Hurwitz groups
Herrlich showed that a Mumford curve of genus g > 1 over the p-adic complex field Cp has at most 48(g− 1), 24(g− 1), 30(g− 1) or 12(g− 1) automorphisms as p = 2, 3, 5 or p > 5. The Mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p-adic triangle groups ∆p for p ≤ 5, or in a p-adic quadrangle group p for p > 5. The finite groups attaining these...
متن کاملSIMPLE p - ADIC GROUPS , II
0.1. For any finite group Γ, a “nonabelian Fourier transform matrix” was introduced in [L1]. This is a square matrix whose rows and columns are indexed by pairs formed by an element of Γ and an irreducible representation of the centralizer of that element (both defined up to conjugation). As shown in [L2], this matrix, which is unitary with square 1, enters (for suitable Γ) in the character for...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2009
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-09-10206-x