Email this article Asymptotics of the Number of Geodesics in the Discrete Heisenberg Group
- Authors: Vershik A.M.1,2, Malyutin A.V.1
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Affiliations:
- St.Petersburg Department of Steklov Institute of Mathematics and St.Petersburg State University
- Institute for Information Transmission Problems
- Issue: Vol 240, No 5 (2019)
- Pages: 525-534
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/242778
- DOI: https://doi.org/10.1007/s10958-019-04370-2
- ID: 242778
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Abstract
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.
About the authors
A. M. Vershik
St.Petersburg Department of Steklov Institute of Mathematics and St.Petersburg State University; Institute for Information Transmission Problems
Author for correspondence.
Email: avershik@pdmi.ras.ru
Russian Federation, St.Petersburg; Moscow
A. V. Malyutin
St.Petersburg Department of Steklov Institute of Mathematics and St.Petersburg State University
Email: avershik@pdmi.ras.ru
Russian Federation, St.Petersburg
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