Ebook: Representation Theories and Algebraic Geometry

The 12 lectures presented in Representation Theories and AlgebraicGeometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology.
The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.

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The 12 lectures presented in Representation Theories and AlgebraicGeometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology.
The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.

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The 12 lectures presented in Representation Theories and AlgebraicGeometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology.
The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.
Content:
Front Matter....Pages i-xxii
Equivariant cohomology and equivariant intersection theory....Pages 1-37
Lectures on decomposition classes....Pages 39-83
Instantons and K?hler geometry of nilpotent orbits....Pages 85-125
Geometric methods in the representation theory of Hecke algebras and quantum groups....Pages 127-183
Representations of Lie algebras in prime characteristic....Pages 185-235
Sur l’annulateur d’un module de Verma....Pages 237-300
Some remarks on multiplicity free spaces....Pages 301-317
Standard Monomial Theory and applications....Pages 319-364
Canonical bases and Hall algebras....Pages 365-399
Combinatorics of Harish-Chandra modules....Pages 401-412
Schubert varieties and generalizations....Pages 413-440
Back Matter....Pages 441-443

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The 12 lectures presented in Representation Theories and AlgebraicGeometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology.
The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.
Content:
Front Matter....Pages i-xxii
Equivariant cohomology and equivariant intersection theory....Pages 1-37
Lectures on decomposition classes....Pages 39-83
Instantons and K?hler geometry of nilpotent orbits....Pages 85-125
Geometric methods in the representation theory of Hecke algebras and quantum groups....Pages 127-183
Representations of Lie algebras in prime characteristic....Pages 185-235
Sur l’annulateur d’un module de Verma....Pages 237-300
Some remarks on multiplicity free spaces....Pages 301-317
Standard Monomial Theory and applications....Pages 319-364
Canonical bases and Hall algebras....Pages 365-399
Combinatorics of Harish-Chandra modules....Pages 401-412
Schubert varieties and generalizations....Pages 413-440
Back Matter....Pages 441-443
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