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TMF, 2013, Volume 174, Number 1, Pages 109–124 (Mi tmf8343)  

This article is cited in 4 scientific papers (total in 4 papers)

An inductive approach to representations of complex reflection groups $G(m,1,n)$

O. V. Ogievetskiiab, L. Poulain d'Andecya

a Centre de Physique Théorique Campus de Luminy, Marseille, France
b Lebedev Physical Institute, RAS, Moscow, Russia

Abstract: We propose an inductive approach to the representation theory of the chain of complex reflection groups $G(m,1,n)$. We obtain the Jucys–Murphy elements of $G(m,1,n)$ from the Jucys–Murphy elements of the cyclotomic Hecke algebra and study their common spectrum using representations of a degenerate cyclotomic affine Hecke algebra. We construct representations of $G(m,1,n)$ using a new associative algebra whose underlying vector space is the tensor product of the group ring $\mathbb{C}G(m,1,n)$ with a free associative algebra generated by the standard $m$-tableaux.

Keywords: group tower, Hecke algebra, reflection group, maximal commutative subalgebra, Young diagram, Young tableau

DOI: https://doi.org/10.4213/tmf8343

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English version:
Theoretical and Mathematical Physics, 2013, 174:1, 95–108

Bibliographic databases:

Received: 04.04.2012

Citation: O. V. Ogievetskii, L. Poulain d'Andecy, “An inductive approach to representations of complex reflection groups $G(m,1,n)$”, TMF, 174:1 (2013), 109–124; Theoret. and Math. Phys., 174:1 (2013), 95–108

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Chlouveraki, L. P. d'Andecy, “Representation theory of the Yokonuma-Hecke algebra”, Adv. Math., 259 (2014), 134–172  crossref  mathscinet  zmath  isi  elib  scopus
    2. O. V. Ogievetsky, L. P. d'Andecy, “Induced representations and traces for chains of affine and cyclotomic Hecke algebras”, J. Geom. Phys., 87 (2015), 354–372  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. L. P. d'Andecy, “Young tableaux and representations of Hecke algebras of type ADE”, J. Comb. Algebra, 1:4 (2017), 371–423  crossref  mathscinet  zmath  isi
    4. O. Ogievetsky, V. Petrova, “Cyclotomic shuffles”, Phys. Part. Nuclei, 49:5 (2018), 867–872  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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