# Journal of the Ramanujan Mathematical Society

Volume 33, Issue 4, December 2018  pp. 435–454.

Zero weight space for tori inside a division algebra

Authors:  Sampath Lonka and Rajat Tandon
Author institution:School of Mathematics and Statistics, University of Hyderabad, Hyderabad 500 046, India

Summary:  Let F be a non-Archimedean local field of residue characteristic p. Consider a division algebra D over F of index ℓ, where ℓ is an odd prime and ℓ ≠ p. Let π be an irreducible representation of D* with trivial central character. Let K/F be any field extension of degree ℓ in D. We compute the complex dimension of K*-invariant vectors of π as both π and K vary.