Asymptotics of the Number of Geodesics in the Discrete Heisenberg Group


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The study of the degenerate part of the absolute of the discrete Heisenberg group required solving a problem on the number of geodesics in this group and in its semigroup. Analytically, this problem reduces to the study of the asymptotic behavior of Gaussian q-binomial coefficients, and the required property is the almost multiplicativity of group characters. The problem has a natural formulation in terms of an (apparently, new) asymptotic property of Young diagrams.

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A. Vershik

St.Petersburg Department of Steklov Institute of Mathematics and St.Petersburg State University; Institute for Information Transmission Problems

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Email: avershik@pdmi.ras.ru
俄罗斯联邦, St.Petersburg; Moscow

A. Malyutin

St.Petersburg Department of Steklov Institute of Mathematics and St.Petersburg State University

Email: avershik@pdmi.ras.ru
俄罗斯联邦, St.Petersburg

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