A note on the representation theory of the Hecke algebra of type <i>F<sub>4</sub></i>

Pallikaros, C. A.

doi:10.1017/s001708950003189x

Cited by 2 publications

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References 4 publications

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“…Indeed, with two exceptions, all the irreducible representations which occurred were equivalent to specializations of some of the 47 representations described in [8]. For explicit realizations of these representations, see [9,10,8].…”

Section: Introductionmentioning

confidence: 99%

On the Irreducible Representations of the Specializations in Characteristics 2 and 3 of the Generic Hecke Algebra of Type F4

McDonough

Pallikaros

2000

Journal of Algebra

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A complete determination of the irreducible modules of specialized Hecke algebras of type F 4 , with respect to specializations with equal parameters, has been obtained by M. Geck and K. Lux (1991, Manuscripta Math. 70, 285-306) for all characteristics. A similar determination for specializations with v = u 2 and v = u 4 has been obtained by K. Bremke (1994, Manuscripta Math. 83, 331-346). In another paper (1999, J. Algebra, 218, 654-671), the authors determined the irreducible modules for all remaining specializations other than those into fields of characteristic 2 or 3, obtaining en route decompositions of the generic irreducible modules under such specializations. In this paper, the corresponding results for characteristic 2 or 3 are obtained. Again, it is found that the decomposition matrices may be expressed in lower uni-triangular form in all these cases and that the splitting fields are those generated by the images of the parameters.

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Section: Introductionmentioning

confidence: 99%

On the Irreducible Representations of the Specializations in Characteristics 2 and 3 of the Generic Hecke Algebra of Type F4

McDonough

Pallikaros

2000

Journal of Algebra

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On the Irreducible Representations of the Specializations of the Generic Hecke Algebra of Type F4

McDonough

Pallikaros

1999

Journal of Algebra

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A complete determination of the irreducible modules of specialized Hecke algebras of type F , with respect to specializations with equal parameters, was 4 Ž . obtained by M. Geck and K. Lux 1991, Manuscripta Math. 70, 285᎐306 . A similar determination for specializations with¨s u 2 and¨s u 4 was obtained by K.Ž . Bremke 1994, Manuscripta Math. 83, 331᎐346 . In this paper, we determine the irreducible modules for all remaining specializations other than those into fields of characteristic 2 or 3, obtaining en route decompositions of the generic irreducible modules under such specializations. We find that the decomposition matrices may be expressed in lower uni-triangular form in all these cases.

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A note on the representation theory of the Hecke algebra of type F₄

Cited by 2 publications

References 4 publications

On the Irreducible Representations of the Specializations in Characteristics 2 and 3 of the Generic Hecke Algebra of Type F4

On the Irreducible Representations of the Specializations in Characteristics 2 and 3 of the Generic Hecke Algebra of Type F4

On the Irreducible Representations of the Specializations of the Generic Hecke Algebra of Type F4

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A note on the representation theory of the Hecke algebra of type F4

Cited by 2 publications

References 4 publications

On the Irreducible Representations of the Specializations in Characteristics 2 and 3 of the Generic Hecke Algebra of Type F4

On the Irreducible Representations of the Specializations in Characteristics 2 and 3 of the Generic Hecke Algebra of Type F4

On the Irreducible Representations of the Specializations of the Generic Hecke Algebra of Type F4

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A note on the representation theory of the Hecke algebra of type F₄