A simplified proof of the reduction point crossing sign formula for Verma modules
The Unitary Dual Problem is one of the most important open problems in mathematics: classify the irreducible unitary representations of a group. That is, classify all irreducible representations admitting a definite invariant Hermitian form. Signatures of invariant Hermitian forms on Verma modules a...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2019 |
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Інститут прикладної математики і механіки НАН України
2019
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| Zitieren: | A simplified proof of the reduction point crossing sign formula for Verma modules / M.St. Denis, W.L. Yee // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 2. — С. 195–202. — Бібліогр.: 7 назв. — англ. |
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Denis, M.St. Yee, W.L. 2023-03-02T19:17:03Z 2023-03-02T19:17:03Z 2019 A simplified proof of the reduction point crossing sign formula for Verma modules / M.St. Denis, W.L. Yee // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 2. — С. 195–202. — Бібліогр.: 7 назв. — англ. 1726-3255 2010 MSC: 22E50, 05E10 https://nasplib.isofts.kiev.ua/handle/123456789/188488 The Unitary Dual Problem is one of the most important open problems in mathematics: classify the irreducible unitary representations of a group. That is, classify all irreducible representations admitting a definite invariant Hermitian form. Signatures of invariant Hermitian forms on Verma modules are important to finding the unitary dual of a real reductive Lie group. By a philosophy of Vogan introduced in [Vog84], signatures of invariant Hermitian forms on irreducible Verma modules may be computed by varying the highest weight and tracking how signatures change at reducibility points (see [Yee05]). At each reducibility point there is a sign ε governing how the signature changes. A formula for ε was first determined in [Yee05] and simplified in [Yee19]. The proof of the simplification was complicated. We simplify the proof in this note. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics A simplified proof of the reduction point crossing sign formula for Verma modules Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
A simplified proof of the reduction point crossing sign formula for Verma modules |
| spellingShingle |
A simplified proof of the reduction point crossing sign formula for Verma modules Denis, M.St. Yee, W.L. |
| title_short |
A simplified proof of the reduction point crossing sign formula for Verma modules |
| title_full |
A simplified proof of the reduction point crossing sign formula for Verma modules |
| title_fullStr |
A simplified proof of the reduction point crossing sign formula for Verma modules |
| title_full_unstemmed |
A simplified proof of the reduction point crossing sign formula for Verma modules |
| title_sort |
simplified proof of the reduction point crossing sign formula for verma modules |
| author |
Denis, M.St. Yee, W.L. |
| author_facet |
Denis, M.St. Yee, W.L. |
| publishDate |
2019 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
The Unitary Dual Problem is one of the most important open problems in mathematics: classify the irreducible unitary representations of a group. That is, classify all irreducible representations admitting a definite invariant Hermitian form. Signatures of invariant Hermitian forms on Verma modules are important to finding the unitary dual of a real reductive Lie group. By a philosophy of Vogan introduced in [Vog84], signatures of invariant Hermitian forms on irreducible Verma modules may be computed by varying the highest weight and tracking how signatures change at reducibility points (see [Yee05]). At each reducibility point there is a sign ε governing how the signature changes. A formula for ε was first determined in [Yee05] and simplified in [Yee19]. The proof of the simplification was complicated. We simplify the proof in this note.
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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188488 |
| citation_txt |
A simplified proof of the reduction point crossing sign formula for Verma modules / M.St. Denis, W.L. Yee // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 2. — С. 195–202. — Бібліогр.: 7 назв. — англ. |
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2025-12-07T18:43:40Z |
| last_indexed |
2025-12-07T18:43:40Z |
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