Electronic ISBN:  9780821877302 
Product Code:  CONM/139.E 
277 pp 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 

Book DetailsContemporary MathematicsVolume: 139; 1992MSC: Primary 14; 17; 20; 22; Secondary 51; 55;
This volume attests to the farreaching influence of KazhdanLusztig 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 KazhdanLusztig 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 KazhdanLusztig theory, including representations of KacMoody Lie algebras, geometry of Schubert varieties, intersection cohomology of stratified spaces, and some new topics such as quantum groups.
ReadershipResearch mathematicians working in Lie theory, algebraic geometry, noncommutative algebra, topology, microlocal analysis, and quantum groups.

Table of Contents

Articles

Brian D. Boe  A counterexample to the GabberJoseph conjecture [ MR 1197826 ]

JeanLuc 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 KazhdanLusztig theories [ MR 1197829 ]

David H. Collingwood and Ronald S. Irving  HarishChandra 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  KazhdanLusztig 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 HarishChandra modules for complex S.S. groups [ MR 1197838 ]

Lex E. Renner  Towards a generalized Bruhat decomposition [ MR 1197839 ]


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This volume attests to the farreaching influence of KazhdanLusztig 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 KazhdanLusztig 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 KazhdanLusztig theory, including representations of KacMoody 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 GabberJoseph conjecture [ MR 1197826 ]

JeanLuc 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 KazhdanLusztig theories [ MR 1197829 ]

David H. Collingwood and Ronald S. Irving  HarishChandra 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  KazhdanLusztig 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 HarishChandra modules for complex S.S. groups [ MR 1197838 ]

Lex E. Renner  Towards a generalized Bruhat decomposition [ MR 1197839 ]