A homological interpretation of Jantzen's sum formula
For a split reductive algebraic group, this paper observes a homological interpretation for Weyl module multiplicities in Jantzen's sum formula. This interpretation involves an Euler characteristic built from Ext groups between integral Weyl modules. The new interpretation makes transparent For...
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| creator | Kulkarni, Upendra |
| description | For a split reductive algebraic group, this paper observes a homological
interpretation for Weyl module multiplicities in Jantzen's sum formula. This
interpretation involves an Euler characteristic built from Ext groups between
integral Weyl modules. The new interpretation makes transparent For GL_n (and
conceivable for other classical groups) a certain invariance of Jantzen's sum
formula under "Howe duality" in the sense of Adamovich and Rybnikov. For GL_n a
simple and explicit general formula is derived for the Euler characteristic
between an arbitrary pair of integral Weyl modules. In light of Brenti's work
on certain R-polynomials, this formula raises interesting questions about the
possibility of relating Ext groups between Weyl modules to Kazhdan-Lusztig
combinatorics. |
| doi_str_mv | 10.48550/arxiv.math/0505371 |
| format | Article |
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interpretation for Weyl module multiplicities in Jantzen's sum formula. This
interpretation involves an Euler characteristic built from Ext groups between
integral Weyl modules. The new interpretation makes transparent For GL_n (and
conceivable for other classical groups) a certain invariance of Jantzen's sum
formula under "Howe duality" in the sense of Adamovich and Rybnikov. For GL_n a
simple and explicit general formula is derived for the Euler characteristic
between an arbitrary pair of integral Weyl modules. In light of Brenti's work
on certain R-polynomials, this formula raises interesting questions about the
possibility of relating Ext groups between Weyl modules to Kazhdan-Lusztig
combinatorics.</description><identifier>DOI: 10.48550/arxiv.math/0505371</identifier><language>eng</language><subject>Mathematics - Representation Theory</subject><creationdate>2005-05</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/math/0505371$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.math/0505371$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kulkarni, Upendra</creatorcontrib><title>A homological interpretation of Jantzen's sum formula</title><description>For a split reductive algebraic group, this paper observes a homological
interpretation for Weyl module multiplicities in Jantzen's sum formula. This
interpretation involves an Euler characteristic built from Ext groups between
integral Weyl modules. The new interpretation makes transparent For GL_n (and
conceivable for other classical groups) a certain invariance of Jantzen's sum
formula under "Howe duality" in the sense of Adamovich and Rybnikov. For GL_n a
simple and explicit general formula is derived for the Euler characteristic
between an arbitrary pair of integral Weyl modules. In light of Brenti's work
on certain R-polynomials, this formula raises interesting questions about the
possibility of relating Ext groups between Weyl modules to Kazhdan-Lusztig
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interpretation for Weyl module multiplicities in Jantzen's sum formula. This
interpretation involves an Euler characteristic built from Ext groups between
integral Weyl modules. The new interpretation makes transparent For GL_n (and
conceivable for other classical groups) a certain invariance of Jantzen's sum
formula under "Howe duality" in the sense of Adamovich and Rybnikov. For GL_n a
simple and explicit general formula is derived for the Euler characteristic
between an arbitrary pair of integral Weyl modules. In light of Brenti's work
on certain R-polynomials, this formula raises interesting questions about the
possibility of relating Ext groups between Weyl modules to Kazhdan-Lusztig
combinatorics.</abstract><doi>10.48550/arxiv.math/0505371</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Representation Theory |
| title | A homological interpretation of Jantzen's sum formula |
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