Characters of the norm-one units of local division algebras of prime degree

Shai Shechter

doi:10.1016/j.jalgebra.2016.11.004

Characters of the norm-one units of local division algebras of prime degree

Shai Shechter

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We give an explicit construction of all complex continuous irreducible characters of the group SL₁(D), where D is a division algebra of prime degree ℓ over a local field of odd residual characteristic different from ℓ. For ℓ odd, we show that all such characters of SL₁(D) are induced from linear characters of compact-open subgroups of SL₁(D). We also compute an explicit formula for the representation zeta function of SL₁(D).

Original language	English
Pages (from-to)	134-165
Number of pages	32
Journal	Journal of Algebra
Volume	474
DOIs	https://doi.org/10.1016/j.jalgebra.2016.11.004
State	Published - 15 Mar 2017

Keywords

Division algebras
Representation growth
Representation theory
Representation zeta function
p-adic analytic groups

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2016.11.004

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title = "Characters of the norm-one units of local division algebras of prime degree",

abstract = "We give an explicit construction of all complex continuous irreducible characters of the group SL1(D), where D is a division algebra of prime degree ℓ over a local field of odd residual characteristic different from ℓ. For ℓ odd, we show that all such characters of SL1(D) are induced from linear characters of compact-open subgroups of SL1(D). We also compute an explicit formula for the representation zeta function of SL1(D).",

keywords = "Division algebras, Representation growth, Representation theory, Representation zeta function, p-adic analytic groups",

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AB - We give an explicit construction of all complex continuous irreducible characters of the group SL1(D), where D is a division algebra of prime degree ℓ over a local field of odd residual characteristic different from ℓ. For ℓ odd, we show that all such characters of SL1(D) are induced from linear characters of compact-open subgroups of SL1(D). We also compute an explicit formula for the representation zeta function of SL1(D).

KW - Division algebras

KW - Representation growth

KW - Representation theory

KW - Representation zeta function

KW - p-adic analytic groups

UR - https://www.scopus.com/pages/publications/85000542362

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DO - 10.1016/j.jalgebra.2016.11.004

M3 - Article

AN - SCOPUS:85000542362

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SP - 134

EP - 165

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Characters of the norm-one units of local division algebras of prime degree

Abstract

Keywords

ASJC Scopus subject areas

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