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On an Upper Bound for the Heat Kernel on SU*(2n)/ Sp(n)

Published online by Cambridge University Press:  20 November 2018

P. Sawyer
P. Sawyer*
Affiliation:
Department of Mathematics, University of Ottawa, Ottawa, Ontario, K1N 6N5
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Abstract

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Jean-Philippe Anker made an interesting conjecture in [2] about the growth of the heat kernel on symmetric spaces of noncompact type. For any symmetric space of noncompact type, we can write

where ϕ0 is the Legendre function and q, "the dimension at infinity", is chosen such that limt—>∞Vt(x) = 1 for all x. Anker's conjecture can be stated as follows: there exists a constant C > 0 such that

where is the set of positive indivisible roots. The behaviour of the function ϕ0 is well known (see [1]).

The main goal of this paper is to establish the conjecture for the spaces SU*(2n)/ Sp(n).

Keywords

Primary: 58G30secondary: 53C3558G11
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 408 - 418
Copyright
Copyright © Canadian Mathematical Society 1994

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