Topic
Subquotient
About: Subquotient is a research topic. Over the lifetime, 163 publications have been published within this topic receiving 1693 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, it was shown that any irreducible admissible representation of G can be realized canonically as a subquotient of a generalized principal series representation.
Abstract: (normalized induction) a generalized principal series representation. When v is unitary, these are the representations occurring in Harish-Chandra's Plancherel formula for G; and for general v they may be expected to play something of the same role in harmonic analysis on G as complex characters do in R n. Langlands has shown tha t any irreducible admissible representation of G can be realized canonically as a subquotient of a generalized principal series representation (Theorem 2.9 below). For these reasons and others (some of which will be discussed below) one would like to understand the reducibility of these representations, and it is this question which motivates the results of this paper. We prove
209 citations
TL;DR: In this paper, the authors address the questions of irreducibility and the coexponents of this subquotient, as well as centralisers in G of certain elements of the coset.
Abstract: Let G be a finite group generated by (pseudo-) reflections in a complex vector space and let g be any linear transformation which normalises G. In an earlier paper, the authors showed how to associate with any maximal eigenspace of an element of the coset gG, a subquotient of G which acts as a reflection group on the eigenspace. In this work, we address the questions of irreducibility and the coexponents of this subquotient, as well as centralisers in G of certain elements of the coset. A criterion is also given in terms of the invariant degrees of G for an integer to be regular for G. A key tool is the investigation of extensions of invariant vector fields on the eigenspace, which leads to some results and questions concerning the geometry of intersections of invariant hypersurfaces.
59 citations
Posted Content•
TL;DR: In this paper, it was shown that the quantized Coulomb branch of quiver gauge theories of Jordan type is a deformation of a subquotient of the Yangian.
Abstract: We study quantized Coulomb branches of quiver gauge theories of Jordan type. We prove that the quantized Coulomb branch is isomorphic to the spherical graded Cherednik algebra in the unframed case, and is isomorphic to the spherical cyclotomic rational Cherednik algebra in the framed case. We also prove that the quantized Coulomb branch is a deformation of a subquotient of the Yangian of the affine $\mathfrak{gl}(1)$.
51 citations
TL;DR: In this paper, the necessary and sufficient conditions for fraction modules to be irreducible are determined, and the necessary conditions for two isomorphic fraction modules over centerless Virasoro algebra V to be isomorphic.
48 citations
6 Jun 2018
TL;DR: In this paper, it was shown that the quantized Coulomb branch of quiver gauge theories of Jordan type is a deformation of a subquotient of the Yangian.
Abstract: We study quantized Coulomb branches of quiver gauge theories of Jordan type. We prove that the quantized Coulomb branch is isomorphic to the spherical graded Cherednik algebra in the unframed case, and is isomorphic to the spherical cyclotomic rational Cherednik algebra in the framed case. We also prove that the quantized Coulomb branch is a deformation of a subquotient of the Yangian of the affine $\mathfrak{gl}(1)$.
40 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 8 |
| 2020 | 5 |
| 2019 | 14 |
| 2018 | 10 |
| 2017 | 9 |
| 2016 | 9 |