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Research Article

On double cosets of groups GL (n) with respect to subgroups of block strictly triangular matrices

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Pages 4620-4632 | Received 07 Jan 2021, Accepted 12 Feb 2021, Published online: 28 Feb 2021

References

  • AA. Kirillov. Elements of the theory of representations. Berlin: Springer-Verlag; 1976.
  • Neretin Yu.A. Categories of symmetries and infinite-dimensional groups. New York (NY): Oxford University Press; 1996.
  • Matsuki T. Double coset decompositions of reductive Lie groups arising from two involutions. J Algebra. 1997;197(1):49–91.
  • Matsuki T. The orbits of affine symmetric spaces under the action of minimal parabolic subgroups. J Math Soc Japan. 1979;31(2):331–357.
  • Iwahori N. Generalized Tits system (Bruhat decomposition) on p-adic semisimple groups. In: Borel A, Mostow GD, editors, Algebraic groups and discontinuous subgroups. Proceedings of the Symposium of Pure Mathematics; Vol. 9, Providence (RI): American Mathematical Society; 1966. p. 71–89.
  • Cook RJ, Thomas AD. Line bundles and homogeneous matrices. Quart J Math Oxford Ser (2). 1979;30(4):423–429.
  • Hitchin N. Riemann surfaces and integrable systems. In: Hitchin NJ, Segal GB, Ward RS, editors, Integrable systems. Oxford: Clarendon Press; 1999. p. 11–52.
  • Tyurin AN. On intersections of quadrics. Russian Math Surveys. 1975;30(6):51–105.
  • Beauville A. Determinantal hypersurfaces. Michigan Math J. 2009;48(1):39-–64.
  • Neretin Yu. A. Multi-operator colligations and multivariate spherical functions. Anal Math Phys. 2011;1(2–3):121–138.
  • Neretin Yu. A. Groups GL(∞) over finite fields and multiplications of double cosets. Preprint, arXiv:2002.09969
  • Barut AO, Raczka R. Theory of group representations and applications. Warsaw: PWN-Polish Scientific Publishers; 1977.
  • Neretin Yu. A. Universal completions of complex classical groups. Funct Anal Appl. 1992;26(4):254–265.