On the representation theory of wreath products of finite groups and symmetric groups

Пушкарев, И. А.

doi:10.1007/bf02175835

Cited by 25 publications

(34 citation statements)

References 5 publications

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“…Let S(λ) denote the irreducible Γ nmodule corresponding to the l-multipartition λ. We will later need the following branching rule [27,Theorem 10]. Proposition 2.1.…”

Section: Wreath Productsmentioning

confidence: 99%

The combinatorics of C⁎-fixed points in generalized Calogero-Moser spaces and Hilbert schemes

Przeździecki¹

2020

Journal of Algebra

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In this paper we study the combinatorial consequences of the relationship between rational Cherednik algebras of type G(l, 1, n), cyclic quiver varieties and Hilbert schemes. We classify and explicitly construct C * -fixed points in cyclic quiver varieties and calculate the corresponding characters of tautological bundles. Furthermore, we give a combinatorial description of the bijections between C * -fixed points induced by the Etingof-Ginzburg isomorphism and Nakajima reflection functors. We apply our results to obtain a new proof as well as a generalization of the q-hook formula.2010 Mathematics Subject Classification. 16G99, 05E10.

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“…Let S(λ) denote the irreducible Γ nmodule corresponding to the l-multipartition λ. We will later need the following branching rule [27,Theorem 10]. Proposition 2.1.…”

Section: Wreath Productsmentioning

confidence: 99%

The combinatorics of C⁎-fixed points in generalized Calogero-Moser spaces and Hilbert schemes

Przeździecki¹

2020

Journal of Algebra

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“…The Jucys-Murphy elements for the wreath product of a finite group by a symmetric group were given in [Pus97]. For our particular case G(r, 1, n), the Jucys-Murphy elements can be written as:…”

Section: The Okounkov-vershik Approachmentioning

confidence: 99%

On representation theory of partition algebras for complex reflection groups

Mishra¹,

Srivastava²

2020

Algebraic Combinatorics

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This paper defines the partition algebra, denoted by T k (r, p, n), for complex reflection group G(r, p, n) acting on k-fold tensor product (C n ) ⊗k , where C n is the reflection representation of G(r, p, n). A basis of the centralizer algebra of this action of G(r, p, n) was given by Tanabe and for p = 1, the corresponding partition algebra was studied by Orellana. We also define a subalgebra T k+ 1 2010 MSC: Primary 05E10, 20F55; Secondary 20C15.

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“…The simple representations of kW are labeled by the set P(m, n); over the complex numbers this is standard (see [22] or [33]) and the same holds for kW by reduction, cf. 2.3.…”

Section: 4mentioning

confidence: 99%

“…2.3. In fact the construction from [33] is also valid over k, since p does not divide |W |, so that we can find bases of irreducible kW -modules given by eigenvectors of Jucys-Murphy elements for the group W cf. [28, §5.3].…”

Section: 4mentioning

confidence: 99%

On the Smoothness of Centres of Rational Cherednik Algebras in Positive Characteristic

Bellamy

Martino

2013

Glasgow Math. J.

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Abstract. In this article we study rational Cherednik algebras at t = 1 in positive characteristic. We study a finite dimensional quotient of the rational Cherednik algebra called the restricted rational Cherednik algebra. When the corresponding pseudo-reflection group belongs to the infinite series G(m, d, n), we describe explicitly the block decomposition of the restricted algebra. We also classify all pseudo-reflection groups for which the centre of the corresponding rational Cherednik algebra is regular for generic values of the deformation parameter.

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On the representation theory of wreath products of finite groups and symmetric groups

Cited by 25 publications

References 5 publications

The combinatorics of C⁎-fixed points in generalized Calogero-Moser spaces and Hilbert schemes

The combinatorics of C⁎-fixed points in generalized Calogero-Moser spaces and Hilbert schemes

On representation theory of partition algebras for complex reflection groups

On the Smoothness of Centres of Rational Cherednik Algebras in Positive Characteristic

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