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|---|---|---|---|
| 001 | EBC3113959 | ||
| 003 | MiAaPQ | ||
| 005 | 20240729124555.0 | ||
| 006 | m o d | | ||
| 007 | cr cnu|||||||| | ||
| 008 | 240724s1991 xx o ||||0 eng d | ||
| 020 |
_a9781470408626 _q(electronic bk.) |
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| 020 | _z9780821825013 | ||
| 035 | _a(MiAaPQ)EBC3113959 | ||
| 035 | _a(Au-PeEL)EBL3113959 | ||
| 035 | _a(CaPaEBR)ebr10918912 | ||
| 035 | _a(OCoLC)922981643 | ||
| 040 |
_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ |
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| 050 | 4 | _aQA171 -- .P377 1991eb | |
| 082 | 0 | _a512/.2 | |
| 100 | 1 | _aWang, J. | |
| 245 | 1 | 0 | _aQuantum Linear Groups. |
| 250 | _a1st ed. | ||
| 264 | 1 |
_aProvidence : _bAmerican Mathematical Society, _c1991. |
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| 264 | 4 | _c©1991. | |
| 300 | _a1 online resource (168 pages) | ||
| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 490 | 1 |
_aMemoirs of the American Mathematical Society ; _vv.89 |
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| 505 | 0 | _aIntro -- Contents -- Introduction -- 1. Quantum Groups -- 1.1. Quantum affine spaces -- 1.2. Quantum groups -- 1.3. Direct products -- 1.4. Closed subgroups -- 1.5. Normal closed subgroups -- 1.6. Kernels and exact sequences -- 1.7. Cartesian squares -- 1.8. Coverings -- 2. Representation Theory of Quantum Groups -- 2.1. Rational representations -- 2.2. Functorial description -- 2.3. Defining matrices -- 2.4. Contragradient modules and tensor products -- 2.5. Characters and character groups -- 2.6. Fixed points -- 2.7. Induction -- 2.8. Injective objects -- 2.9. Exact subgroups of quantum groups -- 2.10. A theorem on central faithfully flat morphisms -- 2.11. The Hochschild-Serre spectral sequence -- 3. Quantum Matrix Spaces -- 3.1. Quadratic algebras -- 3.2. Quasi-Yang-Baxter algebras -- 3.3. Basis theorem for quasi-Yang-Baxter algebras -- 3.4. The quadratic algebras K[A[sup(n0)][sub(q)]] and K[A[sup(n0)][sub(q)]] -- 3.5. The quantum matrix space M[sub(q)](n) -- 3.6. The bialgebra structure on K[M[sub(q)](n)] -- 3.7. Some automorphisms and anti-automorphisms -- 3.8. K[A[sup(n0)][sub(q)]] and K[A[sup(n0)][sub(q)] as K[M[sub(q)](n)]-comodules -- 4. Quantum Determinants -- 4.1. Quantum determinant -- 4.2. First properties of the determinant -- 4.3. Subdeterminants -- 4.4. Laplace expansions -- 4.5. Some commutators, I -- 4.6. The centrality of the determinant -- 5. The Antipode and Quantum Linear Groups -- 5.1. Some commutators, II -- 5.2. Some commutators, III -- 5.3. Quantum general and special linear groups -- 5.4. A property of the antipode -- 6. Some Closed Subgroups -- 6.1. Parabolic and Levi subgroups -- 6.2. Some properties of the parabolic and Levi subgroups -- 6.3. Some remarks -- 6.4. Coadjoint action of the maximal torus and the root system -- 6.5. Character groups of T[sub(q)] and B[sub(q)] -- 7. Frobenius Morphisms and Kernels. | |
| 505 | 8 | _a7.1. Gaussian polynomials -- 7.2. Frobenius morphisms -- 7.3. Infinitesimal subgroups -- 7.4. Some homological properties of GL[sub(q)](n) -- 7.5. Some exact subgroups of GL[sub(q)](n) -- 8. Global Representation Theory -- 8.1. Density of the "big cell -- 8.2. Highest weight modules -- 8.3. Some properties of induced G[sub(q)]-modules -- 8.4. Induction to parabolic subgroups -- 8.5. The semisimple rank 1 case, I -- 8.6. The semisimple rank 1 case, II -- 8.7. The one-to-one correspondence between irreducible modules and dominant weights -- 8.8. Formal characters and their invariance under the Weyl group -- 8.9. Injective modules for Borel subgroups -- 8.10. A finiteness theorem -- Weyl modules -- 9. Infinitesimal Representation Theory -- 9.1. An infinitesimal version of the "density theorem -- 9.2. Highest weight and irreducible representations for (G[sub(q)])[sub(1)]-T and (G[sub(q)])[sub(1)]-B -- 9.3. Irreducible representations of (G[sub(q)])[sub(1)] -- 9.4. The tensor product theorem -- 9.5. Induction to "infinitesimal Borel subgroups -- 9.6. Induction from "infinitesimal Borel subgroups", I -- 9.7. Induction from "infinitesimal Borel subgroups", II -- 9.8. Highest weight categories -- 9.9. Injective modules for (G[sub(q)])[sub(1)] -- 9.10. The Steinberg module -- 10. The Generalization of Certain Important Theorems on the Cohomology of Vector Bundles on the Flag Manifold -- 10.1. An isomorphism theorem and its consequences -- 10.2. Borel-Weil-Bott theorem for small dominant weights -- 10.3. Serre duality and strong linkage principle -- 10.4. Kempf vanishing theorem, good filtrations and Weyl character formula -- 10.5. A coalgebra isomorphism between K[GL[sub(q)](n)] and K[GL-[sub(q)](n)] -- 11. g-Schur Algebras -- 11.1. Polynomial representations of G[sub(q)] -- 11.2. The g-Schur algebra S[sub(q)](n,r). | |
| 505 | 8 | _a11.3. S[sub(q)](n,r) as an endomorphism algebra -- 11.4. On the complete reducibility of G[sub(q)]-modules -- 11.5. S[sub(q)](n,r) as a quasi-hereditary algebra -- 11.6. The generalization of a theorem of J. A. Green -- 11.7. Tensor product theorem for q-Schur algebras -- References. | |
| 588 | _aDescription based on publisher supplied metadata and other sources. | ||
| 590 | _aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. | ||
| 650 | 0 | _aLinear algebraic groups. | |
| 650 | 0 | _aRepresentations of groups. | |
| 650 | 0 | _aGroup schemes (Mathematics). | |
| 655 | 4 | _aElectronic books. | |
| 776 | 0 | 8 |
_iPrint version: _aWang, J. _tQuantum Linear Groups _dProvidence : American Mathematical Society,c1991 _z9780821825013 |
| 797 | 2 | _aProQuest (Firm) | |
| 830 | 0 | _aMemoirs of the American Mathematical Society | |
| 856 | 4 | 0 |
_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3113959 _zClick to View |
| 999 |
_c69490 _d69490 |
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