Modular Irreducible Representations of Weyl Groups of TypeBn

Araujo, José O.; Bigeón, J. J.; Gamondi, R. M.

doi:10.1080/00927870903417547

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2015

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“…Every irreducible representation of a Weyl group of type or can be realized as Macdonald's representation (see Carter [4] or Lusztig [5]). Following Macdonald's ideas, the irreducible modular representations for the symmetric group were constructed in [6] and in [7]; a similar circle of ideas produces the irreducible modular representations for a Weyl group of type . Along these lines, a construction of a Gelfand model for the complex reflection group ( , 1, ) was given in [8], also based on Macdonald's ideas (see [9]).…”

Section: Introductionmentioning

confidence: 99%

Irreducible Modular Representations of the Reflection GroupG(m,1,n)

Araujo

Bratten

Maiarú

2015

Journal of Mathematics

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In an article published in 1980, Farahat and Peel realized the irreducible modular representations of the symmetric group. One year later, Al-Aamily, Morris, and Peel constructed the irreducible modular representations for a Weyl group of typeBn. In both cases, combinatorial methods were used. Almost twenty years later, using a geometric construction based on the ideas of Macdonald, first Aguado and Araujo and then Araujo, Bigeón, and Gamondi also realized the irreducible modular representations for the Weyl groups of typesAnandBn. In this paper, we extend the geometric construction based on the ideas of Macdonald to realize the irreducible modular representations of the complex reflection group of typeG(m,1,n).

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