The characters of the binary modular congruence group

Kutzko, Philip

doi:10.1090/s0002-9904-1973-13269-0

Cited by 8 publications

(16 citation statements)

References 10 publications

(8 reference statements)

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“…Precise definitions of these surfaces and their Cheeger constants are given in Section 5. Using probabilistic methods, Brooks and Zuk in [6] showed that h(Γ N \H) ≤ 0.4402 for sufficiently large N. From (i) of Theorem 3 and inequality (12) in Section 4 we have a sharper bound for the cases N = 3, 3 2 , and 5 r . Further, we have:…”

Section: Introductionmentioning

confidence: 86%

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Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Riemann Surfaces

Lanphier

Rosenhouse

2011

Electron. J. Combin.

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We derive upper and lower bounds on the isoperimetric numbers and bisection widths of a large class of regular graphs of high degree. Our methods are combinatorial and do not require a knowledge of the eigenvalue spectrum. We apply these bounds to random regular graphs of high degree and the Platonic graphs over the rings $\mathbb{Z}_n$. In the latter case we show that these graphs are generally non-Ramanujan for composite $n$ and we also give sharp asymptotic bounds for the isoperimetric numbers. We conclude by giving bounds on the Cheeger constants of arithmetic Riemann surfaces. For a large class of these surfaces these bounds are an improvement over the known asymptotic bounds.

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Section: Introductionmentioning

confidence: 86%

“…For other rings, in particular for R = Z N with N composite, the representations of GL 2 (R) and SL 2 (R) are more complicated. See [12] for a study of the characters of SL 2 (Z p n ), for example.…”

Section: Introductionmentioning

confidence: 99%

Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Riemann Surfaces

Lanphier

Rosenhouse

2011

Electron. J. Combin.

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“…In most cases, these algebras are the Lie algebras of the corresponding group, with SL 2 , p = 2 being a notable exception, as we will see below. For SL 2 with p = 2 this method was employed by Kutzko in his thesis (unpublished, see the announcement [17]) and by Shalika (whose results remained unpublished until recently, cf. [29]).…”

Section: The Unramified Approachmentioning

confidence: 99%

Extended Deligne–Lusztig varieties for general and special linear groups

Stasinski

2011

Advances in Mathematics

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We give a generalisation of Deligne-Lusztig varieties for general and special linear groups over finite quotients of the ring of integers in a nonarchimedean local field. Previously, a generalisation was given by Lusztig by attaching certain varieties to unramified maximal tori inside Borel subgroups. In this paper we associate a family of so-called extended Deligne-Lusztig varieties to all tamely ramified maximal tori of the group.Moreover, we analyse the structure of various generalised Deligne-Lusztig varieties, and show that the "unramified" varieties, including a certain natural generalisation, do not produce all the irreducible representations in general. On the other hand, we prove results which together with some computations of Lusztig show that for SL 2 (Fq[[̟]]/(̟ 2 )), with odd q, the extended Deligne-Lusztig varieties do indeed afford all the irreducible representations.

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“…In a series of papers by Nobs, and Nobs and Wolfart [21,22,[24][25][26], these constructions are generalized in several directions: some of the constructions are applied for p = 2, some of them are valid when Z p is replaced by any ring of integers of a local field, and some are applied to GL 2 . Other publications which do not use the Weil representation include: Kutzko [16] and Nagornyȋ [20] for SL 2 (Z/p Z), Silberger [29] for PGL 2 (o ) and Shalika [28] for SL 2 (o ) when o has characteristic zero. In a more recent paper [13], Jaikin-Zapirain computes the representation zeta function for SL 2 (o) in the case of odd characteristic.…”

Section: History Of the Problemmentioning

confidence: 99%

Representations of automorphism groups of finiteo-modules of rank two

Onn

2008

Advances in Mathematics

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Let o be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite o-module M of rank two. The main emphasis is on the interaction between the different groups and their representations. An induction scheme is developed in order to study the whole family of these groups coherently. The results obtained depend on the ring o in a very weak manner, mainly through the degree of the residue field. In particular, a uniform description of the irreducible representations of GL 2 (o/p ) is obtained, where p is the maximal ideal of o.

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The characters of the binary modular congruence group

Cited by 8 publications

References 10 publications

Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Riemann Surfaces

Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Riemann Surfaces

Extended Deligne–Lusztig varieties for general and special linear groups

Representations of automorphism groups of finiteo-modules of rank two

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