# 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.

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