On Groups Related to the Hecke Groups
نویسندگان
چکیده
منابع مشابه
Generalized Hecke Groups and Hecke Polygons
In this paper, we study certain Fuchsian groups H (p1, . . . , pn) , called generalized Hecke groups. These groups are isomorphic to ∏∗ n j=1Zpj . Let Γ be a subgroup of finite index in H (p1, . . . , pn) . By Kurosh’s theorem, Γ is isomorphic to Fr ∗ ∏∗ k i=1Zmi , where Fr is a free group of rank r , and each mi divides some pj . Moreover, H/Γ is Riemann surface. The numbers m1, . . . , mk are...
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In this paper, we examine some properties of suborbital graphs for the Hecke groups , H ( √ 2); and H ( √ 3) on Q̂; √ 2Q̂; and √ 3Q̂, respectively. In addition, we give necessary and su3cient conditions for the suborbital graph G(∞; (u=n)√m) to be a forest. Finally, we completely 'nd the number of sides of all the circuits in the suborbital graphs. c © 2001 Elsevier Science B.V. All rights reserved.
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We give the first example of a connected 4-regular graph whose Laplace operator’s spectrum is a Cantor set, as well as several other computations of spectra following a common “finite approximation” method. These spectra are simple transforms of the Julia sets associated to some quadratic maps. The graphs involved are Schreier graphs of fractal groups of intermediate growth, and are also “subst...
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We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via categorification. We present results on branching rules and crystal graphs, decomposition numbers and canonical bases, graded representation theory, connections with cyclotomic and affine Hecke alge...
متن کاملOn the Cuspidal Spectrum of the Arithmetic Hecke Groups
Let T{s/m) (m = 1, 2, 3) be the three arithmetic Hecke groups, generated by the translation z >-> z+y/m and the inversion zn-i. (HI) is the modular group PSL(2, Z).) The purpose of this article is to present several theoretical results on £(\/m), the weight-zero cuspidal spectrum of T(\/m), which are of interest from a computational perspective, since they have application to the numerical stud...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1993
ISSN: 0002-9939
DOI: 10.2307/2159826