Journal of the Ramanujan Mathematical Society

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Zero Weight Space for Tori Inside a Division Algebra


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1 School of Mathematics and Statistics, University of Hyderabad, Hyderabad, 500046, India
     

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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 Ξ  be an irreducible representation of Dβˆ— with trivial central character. Let K/F be any field extension of degree 𝓁 in D. We compute the complex dimension of Kβˆ—-invariant vectors of Ο€ as both Ξ  and K vary.
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  • Zero Weight Space for Tori Inside a Division Algebra

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Authors

Sampath Lonka
School of Mathematics and Statistics, University of Hyderabad, Hyderabad, 500046, India
Rajat Tandon
School of Mathematics and Statistics, University of Hyderabad, Hyderabad, 500046, India

Abstract


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 Ξ  be an irreducible representation of Dβˆ— with trivial central character. Let K/F be any field extension of degree 𝓁 in D. We compute the complex dimension of Kβˆ—-invariant vectors of Ο€ as both Ξ  and K vary.

References