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

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• 作者：Shai Shechter ^{shais@post.bgu.ac.il}
• 关键词：Representation theory ; Division algebras ; Representation growth ; p-adic analytic groups ; Representation zeta function
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：474
• 期：Complete
• 页码：134-165
• 全文大小：599 K
• 卷排序：474

文摘

We give an explicit construction of all complex continuous irreducible characters of the group SL1(D)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)SL1(D) are induced from linear characters of compact-open subgroups of SL1(D)SL1(D). We also compute an explicit formula for the representation zeta function of SL1(D)SL1(D).