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Kazhdan-Lusztig Theory and Related Topics

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Electronic ISBN: 978-0-8218-7730-2
Product Code: CONM/139.E
List Price: $59.00 MAA Member Price:$53.10
AMS Member Price: $47.20 Click above image for expanded view Kazhdan-Lusztig Theory and Related Topics Available Formats:  Electronic ISBN: 978-0-8218-7730-2 Product Code: CONM/139.E  List Price:$59.00 MAA Member Price: $53.10 AMS Member Price:$47.20
• Book Details

Contemporary Mathematics
Volume: 1391992; 277 pp
MSC: Primary 14; 17; 20; 22; Secondary 51; 55;

This volume attests to the far-reaching influence of Kazhdan-Lusztig theory on several areas of mathematics by presenting a diverse set of research articles centered on this theme. Although there has been a great deal of work in Kazhdan-Lusztig theory, this book is perhaps the first to discuss all aspects of the theory and gives readers a flavor of the range of topics involved. The articles present recent work in Kazhdan-Lusztig theory, including representations of Kac-Moody Lie algebras, geometry of Schubert varieties, intersection cohomology of stratified spaces, and some new topics such as quantum groups.

Research mathematicians working in Lie theory, algebraic geometry, noncommutative algebra, topology, microlocal analysis, and quantum groups.

• Articles
• Brian D. Boe - A counterexample to the Gabber-Joseph conjecture [ MR 1197826 ]
• Jean-Luc Brylinski - Equivariant intersection cohomology [ MR 1197827 ]
• James B. Carrell - Some remarks on regular Weyl group orbits and the cohomology of Schubert varieties [ MR 1197828 ]
• Edward Cline, Brian Parshall and Leonard Scott - Infinitesimal Kazhdan-Lusztig theories [ MR 1197829 ]
• David H. Collingwood and Ronald S. Irving - Harish-Chandra modules for semisimple Lie groups with one conjugacy class of Cartan subgroups [ MR 1197830 ]
• Romuald Dąbrowski - A simple proof of a necessary and sufficient condition for the existence of nontrivial global sections of a line bundle on a Schubert variety [ MR 1197831 ]
• Jie Du - Kazhdan-Lusztig bases and isomorphism theorems for $q$-Schur algebras [ MR 1197832 ]
• M. J. Dyer - Hecke algebras and shellings of Bruhat intervals. II. Twisted Bruhat orders [ MR 1197833 ]
• I. Grojnowski and G. Lusztig - On bases of irreducible representations of quantum ${\rm GL}_n$ [ MR 1197834 ]
• Timothy J. Hodges - Morita equivalence of primitive factors of $U({\rm sl}(2))$ [ MR 1197835 ]
• C. Huneke and V. Lakshmibai - Degeneracy of Schubert varieties [ MR 1197836 ]
• Ronald S. Irving - Singular blocks of the category $\scr O$. II [ MR 1197837 ]
• Bertram Kostant and Shrawan Kumar - A geometric realization of minimal $\mathfrak {k}$-type of Harish-Chandra modules for complex S.S. groups [ MR 1197838 ]
• Lex E. Renner - Towards a generalized Bruhat decomposition [ MR 1197839 ]
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Volume: 1391992; 277 pp
MSC: Primary 14; 17; 20; 22; Secondary 51; 55;

This volume attests to the far-reaching influence of Kazhdan-Lusztig theory on several areas of mathematics by presenting a diverse set of research articles centered on this theme. Although there has been a great deal of work in Kazhdan-Lusztig theory, this book is perhaps the first to discuss all aspects of the theory and gives readers a flavor of the range of topics involved. The articles present recent work in Kazhdan-Lusztig theory, including representations of Kac-Moody Lie algebras, geometry of Schubert varieties, intersection cohomology of stratified spaces, and some new topics such as quantum groups.

Research mathematicians working in Lie theory, algebraic geometry, noncommutative algebra, topology, microlocal analysis, and quantum groups.

• Articles
• Brian D. Boe - A counterexample to the Gabber-Joseph conjecture [ MR 1197826 ]
• Jean-Luc Brylinski - Equivariant intersection cohomology [ MR 1197827 ]
• James B. Carrell - Some remarks on regular Weyl group orbits and the cohomology of Schubert varieties [ MR 1197828 ]
• Edward Cline, Brian Parshall and Leonard Scott - Infinitesimal Kazhdan-Lusztig theories [ MR 1197829 ]
• David H. Collingwood and Ronald S. Irving - Harish-Chandra modules for semisimple Lie groups with one conjugacy class of Cartan subgroups [ MR 1197830 ]
• Romuald Dąbrowski - A simple proof of a necessary and sufficient condition for the existence of nontrivial global sections of a line bundle on a Schubert variety [ MR 1197831 ]
• Jie Du - Kazhdan-Lusztig bases and isomorphism theorems for $q$-Schur algebras [ MR 1197832 ]
• M. J. Dyer - Hecke algebras and shellings of Bruhat intervals. II. Twisted Bruhat orders [ MR 1197833 ]
• I. Grojnowski and G. Lusztig - On bases of irreducible representations of quantum ${\rm GL}_n$ [ MR 1197834 ]
• Timothy J. Hodges - Morita equivalence of primitive factors of $U({\rm sl}(2))$ [ MR 1197835 ]
• C. Huneke and V. Lakshmibai - Degeneracy of Schubert varieties [ MR 1197836 ]
• Ronald S. Irving - Singular blocks of the category $\scr O$. II [ MR 1197837 ]
• Bertram Kostant and Shrawan Kumar - A geometric realization of minimal $\mathfrak {k}$-type of Harish-Chandra modules for complex S.S. groups [ MR 1197838 ]
• Lex E. Renner - Towards a generalized Bruhat decomposition [ MR 1197839 ]
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