Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / / George Lusztig.
This book presents a classification of all (complex)irreducible representations of a reductive group withconnected centre, over a finite field. To achieve this,the author uses etale intersection cohomology, anddetailed information on representations of Weylgroups.
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1984 |
| Year of Publication: | 2016 |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
107 |
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| Physical Description: | 1 online resource (408 p.) |
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Lusztig, George, author. aut http://id.loc.gov/vocabulary/relators/aut Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / George Lusztig. Princeton, NJ : Princeton University Press, [2016] ©1984 1 online resource (408 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 107 Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- 1. COMPUTATION OF LOCAL INTERSECTION COHOMOLOGY OF CERTAIN LINE BUNDLES OVER A SCHUBERT VARIETY -- 2. LOCAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE CLOSURES OF THE VARIETIES XW -- 3. GLOBAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE VARIETY X̅W -- 4. REPRESENTATIONS OF WEYL GROUPS -- 5. CELLS IN WEYL GROUPS -- 6. AN INTEGRALITY THEOREM AND A DISJOINTNESS THEOREM -- 7. SOME EXCEPTIONAL GROUPS -- 8. DECOMPOSITION OF INDUCED REPRESENTATIONS -- 9. CLASSICAL GROUPS -- 10. COMPLETION OF THE PROOF OF THEOREM 4.23 -- 11. EIGENVALUES OF FROBENIUS -- 12. ON THE STRUCTURE OF LEFT CELLS -- 13. RELATIONS WITH CONJUGACY CLASSES -- 14. CONCLUDING REMARKS -- APPENDIX -- REFERENCES -- SUBJECT INDEX -- NOTATION INDEX -- Backmatter restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This book presents a classification of all (complex)irreducible representations of a reductive group withconnected centre, over a finite field. To achieve this,the author uses etale intersection cohomology, anddetailed information on representations of Weylgroups. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Characters of groups. Finite fields (Algebra). Finite groups. MATHEMATICS / Group Theory. bisacsh Addition. Algebra representation. Algebraic closure. Algebraic group. Algebraic variety. Algebraically closed field. Bijection. Borel subgroup. Cartan subalgebra. Character table. Character theory. Characteristic function (probability theory). Characteristic polynomial. Class function (algebra). Classical group. Coefficient. Cohomology with compact support. Cohomology. Combination. Complex number. Computation. Conjugacy class. Connected component (graph theory). Coxeter group. Cyclic group. Cyclotomic polynomial. David Kazhdan. Dense set. Derived category. Diagram (category theory). Dimension. Direct sum. Disjoint sets. Disjoint union. E6 (mathematics). Eigenvalues and eigenvectors. Endomorphism. Equivalence class. Equivalence relation. Existential quantification. Explicit formula. Explicit formulae (L-function). Fiber bundle. Finite field. Finite group. Fourier transform. Green's function. Group (mathematics). Group action. Group representation. Harish-Chandra. Hecke algebra. Identity element. Integer. Irreducible representation. Isomorphism class. Jordan decomposition. Line bundle. Linear combination. Local system. Mathematical induction. Maximal torus. Module (mathematics). Monodromy. Morphism. Orthonormal basis. P-adic number. Parametrization. Parity (mathematics). Partially ordered set. Perverse sheaf. Pointwise. Polynomial. Quantity. Rational point. Reductive group. Ree group. Schubert variety. Scientific notation. Semisimple Lie algebra. Sheaf (mathematics). Simple group. Simple module. Special case. Standard basis. Subset. Subtraction. Summation. Surjective function. Symmetric group. Tensor product. Theorem. Two-dimensional space. Unipotent representation. Vector bundle. Vector space. Verma module. Weil conjecture. Weyl group. Zariski topology. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691083513 https://doi.org/10.1515/9781400881772 https://www.degruyter.com/isbn/9781400881772 Cover https://www.degruyter.com/document/cover/isbn/9781400881772/original |
| language |
English |
| format |
eBook |
| author |
Lusztig, George, Lusztig, George, |
| spellingShingle |
Lusztig, George, Lusztig, George, Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / Annals of Mathematics Studies ; Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- 1. COMPUTATION OF LOCAL INTERSECTION COHOMOLOGY OF CERTAIN LINE BUNDLES OVER A SCHUBERT VARIETY -- 2. LOCAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE CLOSURES OF THE VARIETIES XW -- 3. GLOBAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE VARIETY X̅W -- 4. REPRESENTATIONS OF WEYL GROUPS -- 5. CELLS IN WEYL GROUPS -- 6. AN INTEGRALITY THEOREM AND A DISJOINTNESS THEOREM -- 7. SOME EXCEPTIONAL GROUPS -- 8. DECOMPOSITION OF INDUCED REPRESENTATIONS -- 9. CLASSICAL GROUPS -- 10. COMPLETION OF THE PROOF OF THEOREM 4.23 -- 11. EIGENVALUES OF FROBENIUS -- 12. ON THE STRUCTURE OF LEFT CELLS -- 13. RELATIONS WITH CONJUGACY CLASSES -- 14. CONCLUDING REMARKS -- APPENDIX -- REFERENCES -- SUBJECT INDEX -- NOTATION INDEX -- Backmatter |
| author_facet |
Lusztig, George, Lusztig, George, |
| author_variant |
g l gl g l gl |
| author_role |
VerfasserIn VerfasserIn |
| author_sort |
Lusztig, George, |
| title |
Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / |
| title_full |
Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / George Lusztig. |
| title_fullStr |
Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / George Lusztig. |
| title_full_unstemmed |
Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / George Lusztig. |
| title_auth |
Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / |
| title_alt |
Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- 1. COMPUTATION OF LOCAL INTERSECTION COHOMOLOGY OF CERTAIN LINE BUNDLES OVER A SCHUBERT VARIETY -- 2. LOCAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE CLOSURES OF THE VARIETIES XW -- 3. GLOBAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE VARIETY X̅W -- 4. REPRESENTATIONS OF WEYL GROUPS -- 5. CELLS IN WEYL GROUPS -- 6. AN INTEGRALITY THEOREM AND A DISJOINTNESS THEOREM -- 7. SOME EXCEPTIONAL GROUPS -- 8. DECOMPOSITION OF INDUCED REPRESENTATIONS -- 9. CLASSICAL GROUPS -- 10. COMPLETION OF THE PROOF OF THEOREM 4.23 -- 11. EIGENVALUES OF FROBENIUS -- 12. ON THE STRUCTURE OF LEFT CELLS -- 13. RELATIONS WITH CONJUGACY CLASSES -- 14. CONCLUDING REMARKS -- APPENDIX -- REFERENCES -- SUBJECT INDEX -- NOTATION INDEX -- Backmatter |
| title_new |
Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / |
| title_sort |
characters of reductive groups over a finite field. (am-107), volume 107 / |
| series |
Annals of Mathematics Studies ; |
| series2 |
Annals of Mathematics Studies ; |
| publisher |
Princeton University Press, |
| publishDate |
2016 |
| physical |
1 online resource (408 p.) Issued also in print. |
| contents |
Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- 1. COMPUTATION OF LOCAL INTERSECTION COHOMOLOGY OF CERTAIN LINE BUNDLES OVER A SCHUBERT VARIETY -- 2. LOCAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE CLOSURES OF THE VARIETIES XW -- 3. GLOBAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE VARIETY X̅W -- 4. REPRESENTATIONS OF WEYL GROUPS -- 5. CELLS IN WEYL GROUPS -- 6. AN INTEGRALITY THEOREM AND A DISJOINTNESS THEOREM -- 7. SOME EXCEPTIONAL GROUPS -- 8. DECOMPOSITION OF INDUCED REPRESENTATIONS -- 9. CLASSICAL GROUPS -- 10. COMPLETION OF THE PROOF OF THEOREM 4.23 -- 11. EIGENVALUES OF FROBENIUS -- 12. ON THE STRUCTURE OF LEFT CELLS -- 13. RELATIONS WITH CONJUGACY CLASSES -- 14. CONCLUDING REMARKS -- APPENDIX -- REFERENCES -- SUBJECT INDEX -- NOTATION INDEX -- Backmatter |
| isbn |
9781400881772 9783110494914 9783110442496 9780691083513 |
| callnumber-first |
Q - Science |
| callnumber-subject |
QA - Mathematics |
| callnumber-label |
QA171 |
| callnumber-sort |
QA 3171 |
| url |
https://doi.org/10.1515/9781400881772 https://www.degruyter.com/isbn/9781400881772 https://www.degruyter.com/document/cover/isbn/9781400881772/original |
| illustrated |
Not Illustrated |
| dewey-hundreds |
500 - Science |
| dewey-tens |
510 - Mathematics |
| dewey-ones |
512 - Algebra |
| dewey-full |
512/.2 |
| dewey-sort |
3512 12 |
| dewey-raw |
512/.2 |
| dewey-search |
512/.2 |
| doi_str_mv |
10.1515/9781400881772 |
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979746993 |
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Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
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Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / |
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