Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory.
- 1st ed.
- 1 online resource (222 pages)
- Contemporary Mathematics ; v.602 .
- Contemporary Mathematics .
Intro -- Chapter 1. Preface -- Kostka systems and exotic -structures for reflection groups -- 1. Introduction -- 2. Notation and preliminaries -- 3. Triangulated subcategories associated to a phylum -- 4. Results from the geometry of generalized Springer correspondences -- 5. Module categories associated to a phylum -- 6. Main results -- References -- The doublet vertex operator superalgebras ( ) and _ -- 1. Introduction -- 2. The vertex (super)algebra ( ) -- 3. On intertwining operators for ( ) -- 4. Classification of irreducible ( )-modules -- 5. The Zhu's algebra ( ( )): =4 +2 -- 6. The triplet vertex algebra _ and its modules -- 7. The doublet vertex superalgebra _. -- References -- Quantum deformations of irreducible representations of ( ) toward the Kronecker problem -- 1. Introduction -- 2. Preliminaries -- 3. Wedge Modules -- 4. Crystal basis for ∧_^( ) -- 5. Construction of _( ) -- 6. Research announcement -- Appendix A. An example -- References -- A Parametric Family of Subalgebras of the Weyl Algebra II. Irreducible Modules -- 1. Introduction -- 2. Modules for Ore Extensions -- 3. Indecomposable _-modules -- 4. Generalized Weight Modules for _ -- 5. Primitive Ideals of _ -- 6. Irreducible _-modules when ( )=0 -- 7. Irreducible _-modules when ( )= > -- 0 -- 8. The Combinatorics of ^( ) -- References -- Generic extensions and composition monoids of cyclic quivers -- 1. Introduction -- 2. The generic extension monoid of \tri_ -- 3. Degenerate composition algebras of \tri_ -- 4. A presentation for the composition monoid of \tri₂ -- References -- Wedge modules for two-parameter quantum groups -- 1. Introduction -- 2. Two-parameter quantum group _( _) and R-matrix. 3. Yang-Baxterization -- 4. ( , )-wedge modules of _( _) -- Acknowledgments -- References -- Blocks of the truncated -Schur algebras of type A -- 1. Introduction -- 2. Jantzen equivalence and blocks -- 3. Combinatorics and Jantzen equivalence for Schur algebras -- Acknowledgement -- References -- Decorated Geometric Crystals, Polyhedral and Monomial Realizations of Crystal Bases -- 1. Introduction -- 2. Crystal and its polyhedral realization -- 3. Decorated geometric crystals -- 4. Explicit form of the decoration _ of type _ -- 5. Ultra-Discretization and Polyhedral Realizations of type _ -- 6. Elementary Characters and Monomial Realization of Crystals -- References -- A survey of equivariant map algebras with open problems -- Introduction -- 1. General equivariant map algebras -- 2. Equivariant map associative algebras -- 3. Equivariant map Lie algebras -- 4. Open problems -- References -- Simplicity and similarity of Kirillov-Reshetikhin crystals -- 1. Introduction -- 2. Review on KR crystals -- 3. Simplicity -- 4. Similarity -- 5. Variations -- References -- Forced gradings and the Humphreys-Verma conjecture -- 1. Introduction -- 2. Preliminaries -- 3. A forced graded version of the Humphreys-Verma conjecture -- 4. Variations on a theorem of Alperin-Collins-Sibley -- 5. The general case -- References.