Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory.

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 _{2, } -- 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 _{2, } and its modules -- 7. The doublet vertex superalgebra _{2, }. -- 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 ( )= &gt -- 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.