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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the correspondence of representations between $GL(n)$ and division algebras


Authors: Joshua Lansky and A. Raghuram
Journal: Proc. Amer. Math. Soc. 131 (2003), 1641-1648
MSC (2000): Primary 22E35, 22E50
Published electronically: December 6, 2002
MathSciNet review: 1950297
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Abstract: For a division algebra $D$ over a $p$-adic field $F,$ we prove that depth is preserved under the correspondence of discrete series representations of $GL_n(F)$ and irreducible representations of $D^*$ by proving that an explicit relation holds between depth and conductor for all such representations. We also show that this relation holds for many (possibly all) discrete series representations of $GL_2(D).$


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Additional Information

Joshua Lansky
Affiliation: Department of Mathematics, 380 Olin Science Building, Bucknell University, Lewisburg, Pennsylvania 17837
Email: jlansky@bucknell.edu

A. Raghuram
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Colaba, Mumbai - 400005, India
Email: raghuram@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06918-6
PII: S 0002-9939(02)06918-6
Received by editor(s): December 19, 2001
Published electronically: December 6, 2002
Communicated by: Rebecca Herb
Article copyright: © Copyright 2002 American Mathematical Society