Representation Theory of a Hecke Algebra of G(r, p, n)

Ariki, Susumu

doi:10.1006/jabr.1995.1292

Cited by 68 publications

(146 citation statements)

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“…Proposition 1.6 of [2] yields the specialization of the parameters of the generic Hecke algebra H(G(2f d, 2, 2)), (x 0 , x 1 ; y 0 , y 1 ; z 0 , z 1 , . .…”

Section: The Groups G(de E 2) E Evenmentioning

confidence: 99%

Blocks and Families for Cyclotomic Hecke Algebras

Chlouveraki

2009

Lecture Notes in Mathematics

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“…Proposition 1.6 of [2] yields the specialization of the parameters of the generic Hecke algebra H(G(2f d, 2, 2)), (x 0 , x 1 ; y 0 , y 1 ; z 0 , z 1 , . .…”

Section: The Groups G(de E 2) E Evenmentioning

confidence: 99%

Blocks and Families for Cyclotomic Hecke Algebras

Chlouveraki

2009

Lecture Notes in Mathematics

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“…We first recall Ariki's model (see [Ar,section 2]), and then introduce another one, simpler for our purpose. Ariki chooses a basis of V (λ, ω) given by the p ω (T), where he chooses for T representatives of the S-orbits on T given by the subset T 0 of tuples of tableaux which satisfy T(1) < bd.…”

Section: The Representations Ofmentioning

confidence: 99%

Automorphisms of complex reflection groups

Marin

Michel

2010

Represent. Theory

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Abstract. Let G ⊂ GL(C r ) be a finite complex reflection group. We show that when G is irreducible, apart from the exception G = S 6 , as well as for a large class of non-irreducible groups, any automorphism of G is the product of a central automorphism and of an automorphism which preserves the reflections. We show further that an automorphism which preserves the reflections is the product of an element of N GL(C r ) (G) and of a "Galois" automorphism: we show that Gal(K/Q), where K is the field of definition of G, injects into the group of outer automorphisms of G, and that this injection can be chosen such that it induces the usual Galois action on characters of G, apart from a few exceptional characters; further, replacing K if needed by an extension of degree 2, the injection can be lifted to Aut(G), and every irreducible representation admits a model which is equivariant with respect to this lifting. Along the way we show that the fundamental invariants of G can be chosen rational.

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“…Specifically, we have shown how to decompose the regular representation into its irreducible constituents. Note that in the literature, there are analoguous methods for indexing these representations (see for example, [5,8,9,11,13]). …”

Section: The Irreducible Representations Of G N M Kmentioning

confidence: 99%