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Lie Groups and Representation Theory
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2021/10/19
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Hiroyoshi Tamori (Hokkaido University)
Classification of type A analogues of minimal representations
(Japanese)
Hiroyoshi Tamori (Hokkaido University)
Classification of type A analogues of minimal representations
(Japanese)
[ Abstract ]
If $\mathfrak{g}$ is a simple Lie algebra not of type A, the enveloping algebra $U(\mathfrak{g})$ has a unique completely prime primitive ideal whose associated variety equals the closure of the minimal nilpotent orbit. The ideal is called the Joseph Ideal. An irreducible admissible representation of a simple Lie group is called minimal if the annihilator of the underlying $(\mathfrak{g},\mathfrak{k})$-modules is given by the Joseph ideal. Minimal representations are known to have simple $\mathfrak{k}$-type decompositions (called pencil), and a simple Lie group has at most two minimal representations up to complex conjugate. In this talk, we consider the type A analogues for the above statements.
If $\mathfrak{g}$ is a simple Lie algebra not of type A, the enveloping algebra $U(\mathfrak{g})$ has a unique completely prime primitive ideal whose associated variety equals the closure of the minimal nilpotent orbit. The ideal is called the Joseph Ideal. An irreducible admissible representation of a simple Lie group is called minimal if the annihilator of the underlying $(\mathfrak{g},\mathfrak{k})$-modules is given by the Joseph ideal. Minimal representations are known to have simple $\mathfrak{k}$-type decompositions (called pencil), and a simple Lie group has at most two minimal representations up to complex conjugate. In this talk, we consider the type A analogues for the above statements.
