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Developments and Retrospectives in Lie Theory

Part of the Developments in Mathematics Book Series (volume 38)

Editors: Mason, Geoffrey; Penkov, Ivan; Wolf, Joseph A.

DOI: 10.1007/978-3-319-09804-3

ISBN: 978-3-319-09803-6

Publisher: Springer International Publishing - Springer Journals

Oct 1, 2014

1 - 10 of 17 Chapters

LitStream

Chapter 1Group Gradings on Lie Algebras, with Applications to Geometry. I

Bahturin, Yuri; Goze, Michel; Remm, Elisabeth

Pages: 1 –50

[In this article, which is the first part of a sequence of two, we discuss modern approaches to the classification of group gradings on simple and nilpotent Lie algebras. In the second article we discuss applications and related topics in differential geometry.]
LitStream

Chapter 2Bounding the Dimensions of Rational Cohomology Groups

Bendel, Christopher P.; Boe, Brian D.; Drupieski, Christopher M.; Nakano, Daniel K.; Parshall, Brian J.; Pillen, Cornelius; Wright, Caroline B.

Pages: 51 –69

[Let k be an algebraically closed field of characteristic p > 0, and let G be a simple simply-connected algebraic group over k. In this paper we investigate situations where the dimension of a rational cohomology group for G can be bounded by a constant times the dimension of the coefficient...
LitStream

Chapter 3Representations of the General Linear Lie Superalgebra in the BGG Category 𝒪\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{O}$$ \end{document}

Brundan, Jonathan

Pages: 71 –98

[This is a survey of some recent developments in the highest weight repesentation theory of the general linear Lie superalgebra 𝔤𝔩n|m(ℂ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Chapter 4Three Results on Representations of Mackey Lie Algebras

Chirvasitu, Alexandru

Pages: 99 –109

[I. Penkov and V. Serganova have recently introduced, for any nondegenerate pairing W⊗V→ℂ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 5Free Field Realizations of the Date-Jimbo-Kashiwara-Miwa Algebra

Cox, Ben; Futorny, Vyacheslav; Martins, Renato Alessandro

Pages: 111 –136

[We use the description of the universal central extension of the DJKM algebra 𝔰𝔩(2,R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 6The Deformation Complex is a Homotopy Invariant of a Homotopy Algebra

Dolgushev, Vasily; Willwacher, Thomas

Pages: 137 –158

[To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that ∞-quasi-isomorphic homotopy algebras have L∞-quasiisomorphic deformation complexes by an explicit construction.]
LitStream

Chapter 7Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

Eastwood, Michael; Isaev, Alexander

Pages: 159 –173

[We survey our recently proposed method for constructing biholomorphic invariants of quasihomogeneous isolated hypersurface singularities and, more generally, invariants of graded Artinian Gorenstein algebras. The method utilizes certain polynomials associated to such algebras, called...
LitStream

Chapter 8Generalized Loop Modules for Affine Kac–Moody Algebras

Futorny, Vyacheslav; Kashuba, Iryna

Pages: 175 –183

[We construct new families of irreducible modules for any affine Kac–Moody algebra by considering the parabolic induction from irreducible modules over the Heisenberg subalgebra with a nonzero central charge.]
LitStream

Chapter 9Twisted Localization of Weight Modules

Grantcharov, Dimitar

Pages: 185 –206

[We discuss how the twisted localization functor leads to a classification of the simple objects and a description of the injectives in various categories of weight modules. The article is a survey on existing results for finite-dimensional simple Lie algebras and superalgebras, affine Lie...
LitStream

Chapter 10Dirac Cohomology and Generalization of Classical Branching Rules

Huang, Jing-Song

Pages: 207 –228

[We generalize certain classical results on branching rules such as the Littlewood restriction formulae. Our formulae are expressed in terms of a linear integral combination of the Littlewood–Richardson coefficients and in terms of Dirac cohomology.]

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