-types common to a Borel-de Siebenthal discrete series and its associated holomorphic discrete series

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• 作者：Pampa Paul ^{pampa@imsc.res.in} ; K.N. Raghavan ^{knr@imsc.res.in} ; Parameswaran Sankaran ^{sankaran@imsc.res.in}
• 刊名：Comptes Rendus Mathematique
• 出版年：2012
• 出版时间：December, 2012
• 年：2012
• 卷：350
• 期：23-24
• 页码：1007-1009
• 全文大小：141 K

文摘

Let be a simply connected non-compact real simple Lie group and let be a maximal compact subgroup of . Suppose that is semisimple and that . Let be a Borel-de Siebenthal positive root system and let be the Borel-de Siebenthal discrete series of with Harish-Chandra parameter ¦Ë. One has a certain subgroup so that is an irreducible Hermitian symmetric space. Also, there is a holomorphic discrete series of , the non-compact dual of , with Harish-Chandra parameter , where the sum is over non-compact roots in . We prove that there are infinitely many -types common to and under certain hypotheses.