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Generalized Verma modules induced from characters of parabolic subalgebras with commutative nilpotent radical

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Please use this identifier to cite or link to this item:http://doi.org/10.11501/3159780

Title: Generalized Verma modules induced from characters of parabolic subalgebras with commutative nilpotent radical
Other Titles: 可換な巾零根基をもつ放物型部分代数の指標から誘導された一般化されたバーマ加群
Authors: Wachi, Akihito1 Browse this author
Authors(alt): 和地, 輝仁1
Issue Date: 30-Sep-1999
Abstract: On a scalar generalized Verma module M(λ)= U(g) ⊗U(p) Cλ, the contravariant forms deeply relate to its structure. In this thesis, we show intrinsically that the contravariant forms have b-functions in its factor in the case where g is simple and the nilpotent radical of p is commutative. As an application we explain intrinsically why the b-functions control the irreducibility of M(λ), the orbit decomposition of n+ under the action of the Levi subgroup, and the unitarizability of the irreducible quotient of M(λ). In addition, we construct an analogue on M(λ) the Capelli identity using our main theorem.
Conffering University: 北海道大学
Degree Report Number: 甲第4917号
Degree Level: 博士
Degree Discipline: 理学
Type: theses (doctoral)
URI: http://hdl.handle.net/2115/51621
Appears in Collections:学位論文 (Theses) > 博士 (理学)

Submitter: 和地 輝仁

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