Topics in Computational Algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1990
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The main purpose of these lectures is first to briefly survey the fundamental con nection between the representation theory of the symmetric group Sn and the theory of symmetric functions and second to show how combinatorial methods that arise naturally in the theory of symmetric functions lead to efficient algorithms to express various prod ucts of representations of Sn in terms of sums of irreducible representations. That is, there is a basic isometry which maps the center of the group algebra of Sn, Z(Sn), to the space of homogeneous symmetric functions of degree n, An. This basic isometry is known as the Frobenius map, F. The Frobenius map allows us to reduce calculations involving characters of the symmetric group to calculations involving Schur functions. Now there is a very rich and beautiful theory of the combinatorics of symmetric functions that has been developed in recent years. The combinatorics of symmetric functions, then leads to a number of very efficient algorithms for expanding various products of Schur functions into a sum of Schur functions. Such expansions of products of Schur functions correspond via the Frobenius map to decomposing various products of irreducible representations of Sn into their irreducible components. In addition, the Schur functions are also the characters of the irreducible polynomial representations of the general linear group over the complex numbers GLn(C) |
| Physical Description: | 1 Online-Ressource (V, 261 p) |
| ISBN: | 9789401134248 9789401055147 |
| DOI: | 10.1007/978-94-011-3424-8 |
Staff View
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| 500 | |a The main purpose of these lectures is first to briefly survey the fundamental con nection between the representation theory of the symmetric group Sn and the theory of symmetric functions and second to show how combinatorial methods that arise naturally in the theory of symmetric functions lead to efficient algorithms to express various prod ucts of representations of Sn in terms of sums of irreducible representations. That is, there is a basic isometry which maps the center of the group algebra of Sn, Z(Sn), to the space of homogeneous symmetric functions of degree n, An. This basic isometry is known as the Frobenius map, F. The Frobenius map allows us to reduce calculations involving characters of the symmetric group to calculations involving Schur functions. Now there is a very rich and beautiful theory of the combinatorics of symmetric functions that has been developed in recent years. The combinatorics of symmetric functions, then leads to a number of very efficient algorithms for expanding various products of Schur functions into a sum of Schur functions. Such expansions of products of Schur functions correspond via the Frobenius map to decomposing various products of irreducible representations of Sn into their irreducible components. In addition, the Schur functions are also the characters of the irreducible polynomial representations of the general linear group over the complex numbers GLn(C) | ||
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Record in the Search Index
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| author_facet | Cattaneo, G. M. Piacentini |
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| author_sort | Cattaneo, G. M. Piacentini |
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| ctrlnum | (OCoLC)1165607536 (DE-599)BVBBV042423903 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-011-3424-8 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401134248 9789401055147 |
| language | English |
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| spelling | Cattaneo, G. M. Piacentini Verfasser aut Topics in Computational Algebra edited by G. M. Piacentini Cattaneo, E. Strickland Dordrecht Springer Netherlands 1990 1 Online-Ressource (V, 261 p) txt rdacontent c rdamedia cr rdacarrier The main purpose of these lectures is first to briefly survey the fundamental con nection between the representation theory of the symmetric group Sn and the theory of symmetric functions and second to show how combinatorial methods that arise naturally in the theory of symmetric functions lead to efficient algorithms to express various prod ucts of representations of Sn in terms of sums of irreducible representations. That is, there is a basic isometry which maps the center of the group algebra of Sn, Z(Sn), to the space of homogeneous symmetric functions of degree n, An. This basic isometry is known as the Frobenius map, F. The Frobenius map allows us to reduce calculations involving characters of the symmetric group to calculations involving Schur functions. Now there is a very rich and beautiful theory of the combinatorics of symmetric functions that has been developed in recent years. The combinatorics of symmetric functions, then leads to a number of very efficient algorithms for expanding various products of Schur functions into a sum of Schur functions. Such expansions of products of Schur functions correspond via the Frobenius map to decomposing various products of irreducible representations of Sn into their irreducible components. In addition, the Schur functions are also the characters of the irreducible polynomial representations of the general linear group over the complex numbers GLn(C) Mathematics Electronic data processing Algebra Combinatorics Numeric Computing Datenverarbeitung Mathematik Computeralgebra (DE-588)4010449-7 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1990 Rom gnd-content Computeralgebra (DE-588)4010449-7 s 2\p DE-604 Strickland, E. Sonstige oth https://doi.org/10.1007/978-94-011-3424-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cattaneo, G. M. Piacentini Topics in Computational Algebra Mathematics Electronic data processing Algebra Combinatorics Numeric Computing Datenverarbeitung Mathematik Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4010449-7 (DE-588)1071861417 |
| title | Topics in Computational Algebra |
| title_auth | Topics in Computational Algebra |
| title_exact_search | Topics in Computational Algebra |
| title_full | Topics in Computational Algebra edited by G. M. Piacentini Cattaneo, E. Strickland |
| title_fullStr | Topics in Computational Algebra edited by G. M. Piacentini Cattaneo, E. Strickland |
| title_full_unstemmed | Topics in Computational Algebra edited by G. M. Piacentini Cattaneo, E. Strickland |
| title_short | Topics in Computational Algebra |
| title_sort | topics in computational algebra |
| topic | Mathematics Electronic data processing Algebra Combinatorics Numeric Computing Datenverarbeitung Mathematik Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Mathematics Electronic data processing Algebra Combinatorics Numeric Computing Datenverarbeitung Mathematik Computeralgebra Konferenzschrift 1990 Rom |
| url | https://doi.org/10.1007/978-94-011-3424-8 |
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