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Gelfand-Raikov representations of Coxeter groups associated with positive definite norm functions

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Abstrakty
EN
The main purpose of the paper is to study the type of Gelfand-Raikov representations of Coxeter groups (W, S) for the special positive definite functions coming from the deformed Poisson (Haagerup) positive definite functions qL(w) for some special length (norm) functions L on Coxeter groups W.
Rocznik
Strony
161--180
Opis fizyczny
Bibliogr. 23 poz., tab.
Twórcy
autor
  • Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
autor
  • 22-8 Nakazaichi-Cho, Iwakura, Sakyo-Ku, Kyoto 606-0027, Japan
Bibliografia
  • [1] M. Anshelevich, S. T. Belinschi, M. Bożejko, and F. Lehner, Free infinite divisibility for Q-Gaussians, Math. Res. Lett. 17 (2010), pp. 905-916.
  • [2] S. T. Belinschi, M. Bożejko, F. Lehner, and R. Speicher, The normal distribution is +-infinitely divisible, Adv. Math. 226 (4) (2011), pp. 3677-3698.
  • [3] P. Biane, Representations of symmetric groups and free probability, Adv. Math. 138 (1998), pp. 126-181.
  • [4] P. Biane, F. Goodman, and A. Nica, Non-crossing cumulants of type B, Trans. Amer. Math. Soc. 355 (6) (2003), pp. 2263-2303.
  • [5] M. Bożejko, Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality, Studia Math. 95 (2) (1989), pp. 107-118.
  • [6] M. Bożejko, Deformed Fock spaces, Hecke operators and monotone Fock space of Muraki, Demonstratio Math. 45 (2) (2012), pp. 399-413.
  • [7] M. Bożejko and W. Bożejko, Generalized Gaussian processes and relations with random matrices and positive definite functions on permutation groups, arXiv: 1301.2502.
  • [8] M. Bożejko and M. Guta, Functors of white noise associated to characters of the Infinite symmetric group, Comm. Math. Phys. 229 (2002), pp. 209-227.
  • [9] M. Bożejko and T. Hasebe, On free infinite divisibility for classical Meixner distributions, Probab. Math. Statist. 33 (2) (2013), pp. 363-375.
  • [10] M. Bożejko, T. Januszkiewicz, and R. Spatzier, Infinite Coxeter groups do not have Kazdan’s property, J. Operator Theory 19 (1988), pp. 63-68.
  • [11] M. Bożejko, E. Lytvynov, and J . Wysoczański, Noncommutative Lévy processes for generalized (particularly anyon) statistics, Comm. Math. Phys. 313 (2) (2012), pp. 535-569.
  • [12] M. Bożejko and R. Speicher, Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces, Math. Ann. 300 (1994), pp. 97-120.
  • [13] M. Bożejko and R. Speicher, Interpolations between bosonic and fermionic relations given by generalized Brownian motions, Math. Z. 222 (1996), pp. 135-160.
  • [14] G. Fendler, Central limit theorems for Coxeter systems and Artin systems of extra large type, Heidelberg and arXiv 2003.
  • [15] I. M. Gelfand and D. A. Raikov, Irreducible unitary representations of locally bicompact groups, Amer. Math. Soc. Transl. 36 (1964), pp. 1-15. Original Russian paper: Mat. Sb. 13 (55) (1943), pp. 301-315.
  • [16] M. Guta and H. Maassen, Generalized Brownian motion and second quantization, J. Funct. Anal. 191 (2002), pp. 241-275.
  • [17] T. Hirai, Centralization of positive definite functions, weak containment of representations and Thoma characters for the infinite symmetric group, J. Math. Kyoto Univ. 44 (2004), pp. 685-713.
  • [18] T. Hirai and E. Hirai, Characters for the infinite Weyl groups of type B∞/C∞ and D∞, and for analogous groups, in: Non-Commutativity, Infinite-Dimensionality and Probability at the Crossroad, World Scientific, 2002, pp. 296-317.
  • [19] T. Hirai and E. Hirai, Characters of wreath products of finite groups with the infinite symmetric group, J. Math. Kyoto Univ. 45 (2005), pp. 547-597.
  • [20] A. Hora, Representations of symmetric groups and asymptotic combinatorics (in Japanese), Sūgaku 57 (2005), pp. 242-254. English translation: Sugaku Expositions 22 (2009), pp. 91-106.
  • [21] J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Stud. Adv. Math., Vol. 29, Cambridge University Press, Cambridge 1997.
  • [22] A. Yu. Okounkov, Thoma’s theorem and representations of the infinite bisymmetric group (in Russian), Funktsional. Anal. i Prilozhen. 28 (1994), pp. 31-40. English translation: Funct. Anal. Appl. 28 (1994), pp. 100-107.
  • [23] P. Śniady, Factoriality of Bożejko-Speicher von Neumann algebras, Comm. Math. Phys. 246 (3) (2004), pp. 561-567.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9e61da5b-7f16-4c66-8f91-0f6b610d062e
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