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RELATING TENSOR STRUCTURES ON REPRESENTATIONS OF GENERAL LINEAR AND SYMMETRIC GROUPS
For polynomial representations of GL n of a fixed degree, H. Krause defined a new “internal tensor product” using the language of strict polynomial functors. We show that over an arbitrary commutative base ring k , the Schur functor carries this internal tensor product to the usual Kronecker tensor...
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| Published in: | Transformation groups 2018-06, Vol.23 (2), p.437-461 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c316t-5d23d420acf3fe0394fd3441cb38531a80d8b5203c89c6db62284c66ff60afcc3 |
| container_end_page | 461 |
| container_issue | 2 |
| container_start_page | 437 |
| container_title | Transformation groups |
| container_volume | 23 |
| creator | KULKARNI, UPENDRA SRIVASTAVA, SHRADDHA SUBRAHMANYAM, K. V. |
| description | For polynomial representations of GL
n
of a
fixed
degree, H. Krause defined a new “internal tensor product” using the language of strict polynomial functors. We show that over an arbitrary commutative base ring
k
, the Schur functor carries this internal tensor product to the usual Kronecker tensor product of symmetric group representations. This is true even at the level of derived categories. The new tensor product is a substantial enrichment of the Kronecker tensor product. E.g., in modular representation theory it brings in homological phenomena not visible on the symmetric group side. We calculate the internal tensor product over any commutative ring
k
in several interesting cases involving classical functors and the Weyl functors. We show an application to the Kronecker problem in characteristic zero when one partition has two rows or is a hook. |
| doi_str_mv | 10.1007/s00031-018-9481-x |
| format | article |
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n
of a
fixed
degree, H. Krause defined a new “internal tensor product” using the language of strict polynomial functors. We show that over an arbitrary commutative base ring
k
, the Schur functor carries this internal tensor product to the usual Kronecker tensor product of symmetric group representations. This is true even at the level of derived categories. The new tensor product is a substantial enrichment of the Kronecker tensor product. E.g., in modular representation theory it brings in homological phenomena not visible on the symmetric group side. We calculate the internal tensor product over any commutative ring
k
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n
of a
fixed
degree, H. Krause defined a new “internal tensor product” using the language of strict polynomial functors. We show that over an arbitrary commutative base ring
k
, the Schur functor carries this internal tensor product to the usual Kronecker tensor product of symmetric group representations. This is true even at the level of derived categories. The new tensor product is a substantial enrichment of the Kronecker tensor product. E.g., in modular representation theory it brings in homological phenomena not visible on the symmetric group side. We calculate the internal tensor product over any commutative ring
k
in several interesting cases involving classical functors and the Weyl functors. We show an application to the Kronecker problem in characteristic zero when one partition has two rows or is a hook.</description><subject>Algebra</subject><subject>Group theory</subject><subject>Homology</subject><subject>Lie Groups</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Polynomials</subject><subject>Representations</subject><subject>Topological Groups</subject><subject>Traveling salesman problem</subject><issn>1083-4362</issn><issn>1531-586X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kE9Lw0AQxYMoWKsfwNuC5-jsn2w3xxDXGEg3ZZOAnpZ0kxWLtjVpoX57t1Tw5Gkew--9GV4Q3GK4xwCzhxEAKA4BizBmAoeHs2CCI7-JBH859xoEDRnl5DK4GscVAJ5xzidBrWWR1LnKUC1VVWpU1bpJ60bLCpUKabnwSqraM6XyqyeUSSV1UqAiVzLRKFGPqHqdz2Wt8xRlumwW1XVw4dqPsb_5ndOgeZJ1-hwWZZanSRFaivkujDpCO0agtY66HmjMXEcZw3ZJhX-9FdCJZUSAWhFb3i05IYJZzp3j0Dpr6TS4O-Vuh83Xvh93ZrXZD2t_0hBgnp5FsfAUPlF22Izj0DuzHd4_2-HbYDDH8sypPOPLM8fyzMF7yMkzenb91g9_yf-bfgCqqmrc</recordid><startdate>20180601</startdate><enddate>20180601</enddate><creator>KULKARNI, UPENDRA</creator><creator>SRIVASTAVA, SHRADDHA</creator><creator>SUBRAHMANYAM, K. V.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180601</creationdate><title>RELATING TENSOR STRUCTURES ON REPRESENTATIONS OF GENERAL LINEAR AND SYMMETRIC GROUPS</title><author>KULKARNI, UPENDRA ; SRIVASTAVA, SHRADDHA ; SUBRAHMANYAM, K. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-5d23d420acf3fe0394fd3441cb38531a80d8b5203c89c6db62284c66ff60afcc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algebra</topic><topic>Group theory</topic><topic>Homology</topic><topic>Lie Groups</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Polynomials</topic><topic>Representations</topic><topic>Topological Groups</topic><topic>Traveling salesman problem</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>KULKARNI, UPENDRA</creatorcontrib><creatorcontrib>SRIVASTAVA, SHRADDHA</creatorcontrib><creatorcontrib>SUBRAHMANYAM, K. V.</creatorcontrib><collection>CrossRef</collection><jtitle>Transformation groups</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>KULKARNI, UPENDRA</au><au>SRIVASTAVA, SHRADDHA</au><au>SUBRAHMANYAM, K. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>RELATING TENSOR STRUCTURES ON REPRESENTATIONS OF GENERAL LINEAR AND SYMMETRIC GROUPS</atitle><jtitle>Transformation groups</jtitle><stitle>Transformation Groups</stitle><date>2018-06-01</date><risdate>2018</risdate><volume>23</volume><issue>2</issue><spage>437</spage><epage>461</epage><pages>437-461</pages><issn>1083-4362</issn><eissn>1531-586X</eissn><abstract>For polynomial representations of GL
n
of a
fixed
degree, H. Krause defined a new “internal tensor product” using the language of strict polynomial functors. We show that over an arbitrary commutative base ring
k
, the Schur functor carries this internal tensor product to the usual Kronecker tensor product of symmetric group representations. This is true even at the level of derived categories. The new tensor product is a substantial enrichment of the Kronecker tensor product. E.g., in modular representation theory it brings in homological phenomena not visible on the symmetric group side. We calculate the internal tensor product over any commutative ring
k
in several interesting cases involving classical functors and the Weyl functors. We show an application to the Kronecker problem in characteristic zero when one partition has two rows or is a hook.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00031-018-9481-x</doi><tpages>25</tpages></addata></record> |
| fulltext | fulltext |
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| ispartof | Transformation groups, 2018-06, Vol.23 (2), p.437-461 |
| issn | 1083-4362 1531-586X |
| language | eng |
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| source | Springer Nature |
| subjects | Algebra Group theory Homology Lie Groups Mathematics Mathematics and Statistics Polynomials Representations Topological Groups Traveling salesman problem |
| title | RELATING TENSOR STRUCTURES ON REPRESENTATIONS OF GENERAL LINEAR AND SYMMETRIC GROUPS |
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