Volume: 623; 2014; 280 pp; Softcover
MSC: Primary 14; 16; 17; 20; 81;
Print ISBN: 978-0-8218-9852-9
Product Code: CONM/623
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Electronic ISBN: 978-1-4704-1929-5
Product Code: CONM/623.E
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Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics
Share this pageEdited by Pramod N. Achar; Dijana Jakelić; Kailash C. Misra; Milen Yakimov
This volume contains the proceedings of two
AMS Special Sessions “Geometric and Algebraic Aspects of
Representation Theory” and “Quantum Groups and Noncommutative
Algebraic Geometry” held October 13–14, 2012, at Tulane
University, New Orleans, Louisiana.
Included in this volume are original research and some survey
articles on various aspects of representations of algebras including
Kac–Moody algebras, Lie superalgebras, quantum groups, toroidal
algebras, Leibniz algebras and their connections with other areas of
mathematics and mathematical physics.
Readership
Graduate students and research mathematicians interested in representation theory.
Table of Contents
Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics
- Preface vii8 free
- A classification of irreducible Wakimoto modules for the affine Lie algebra 𝐴₁⁽¹⁾ 114 free
- A note on 𝑈_{𝑞}(𝐷₄⁽³⁾)-Demazure crystals 1326
- Dimensions of imaginary root spaces of hyperbolic Kac–Moody algebras 2336
- 1. Introduction 2336
- 2. Berman-Moody formula and Peterson formula 2538
- 3. Works of Feingold and Frenkel, and Kac, Moody and Wakimoto 2740
- 4. Kang’s generalizations 2841
- 5. Frenkel’s conjecture 3144
- 6. Multiplicities of norm zero root spaces 3245
- 7. Extended and overextended Dynkin diagrams 3245
- 8. Root multiplicities for 𝐸₁₀ and 𝐸₁₁ 3346
- 9. Borcherds’s constructions 3346
- 10. Asymptotics by the method of Hardy-Ramanujan-Rademacher 3548
- 11. Summary of results on root multiplicities 3649
- Acknowledgments 3750
- References 3750
- On some structures of Leibniz algebras 4154
- A geometric construction of generalized 𝑞-Schur algebras 5568
- On the classification of irreducible Gelfand-Tsetlin modules of 𝔰𝔩(3) 6376
- Supersymmetry and the modular double 8194
- On Weyl modules for quantum and hyper loop algebras 99112
- Toroidal Lie superalgebras and free field representations 135148
- Invariants of (-1)-skew polynomial rings under permutation representations 155168
- On total Frobenius-Schur indicators 193206
- Loop Grassmannians in the framework of local spaces over a curve 215228
- Decorated geometric crystals and polyhedral realizations of type 𝐷_{𝑛} 227240
- Some Koszul properties of standard and irreducible modules 243256
- 1. Introduction 243256
- 2. Preliminaries 245258
- 3. A review of some earlier results 249262
- 4. Some new properties of Koszul and Q-Koszul algebras 252265
- 5. A graded Ext result for 𝐺₁𝑇 256269
- 6. Some relative results 258271
- 7. Open questions 260273
- 8. Appendix: Comparison of gradings 261274
- References 263276
- On higher order Leibniz identities in TCFT 267280