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...
Збережено в:
| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188488 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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.
|
|---|---|
| ISSN: | 1726-3255 |