Equivariant Analytic Localization of Group Representations
Seiten
2001
American Mathematical Society (Verlag)
9780821827253 (ISBN)
American Mathematical Society (Verlag)
9780821827253 (ISBN)
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In 1990, Henryk Hecht and Joseph Taylor introduced a technique called analytic localization which vastly generalized the Borel-Weil theorem. This paper develops a refinement of the Hecht-Taylor method, called equivariant analytic localization. It also discusses the advantages that equivariant analytic localization has over analytic localization.
The problem of producing geometric constructions of the linear representations of a real connected semisimple Lie group with finite center, $G_0$, has been of great interest to representation theorists for many years now. A classical construction of this type is the Borel-Weil theorem, which exhibits each finite dimensional irreducible representation of $G_0$ as the space of global sections of a certain line bundle on the flag variety $X$ of the complexified Lie algebra $/mathfrak g$ of $G_0$.In 1990, Henryk Hecht and Joseph Taylor introduced a technique called analytic localization which vastly generalized the Borel-Weil theorem. Their method is similar in spirit to Beilinson and Bernstein's algebraic localization method, but it applies to $G_0$ representations themselves, instead of to their underlying Harish-Chandra modules. For technical reasons, the equivalence of categories implied by the analytic localization method is not as strong as it could be. In this paper, a refinement of the Hecht-Taylor method, called equivariant analytic localization, is developed. The technical advantages that equivariant analytic localization has over (non-equivariant) analytic localization are discussed and applications are indicated.
The problem of producing geometric constructions of the linear representations of a real connected semisimple Lie group with finite center, $G_0$, has been of great interest to representation theorists for many years now. A classical construction of this type is the Borel-Weil theorem, which exhibits each finite dimensional irreducible representation of $G_0$ as the space of global sections of a certain line bundle on the flag variety $X$ of the complexified Lie algebra $/mathfrak g$ of $G_0$.In 1990, Henryk Hecht and Joseph Taylor introduced a technique called analytic localization which vastly generalized the Borel-Weil theorem. Their method is similar in spirit to Beilinson and Bernstein's algebraic localization method, but it applies to $G_0$ representations themselves, instead of to their underlying Harish-Chandra modules. For technical reasons, the equivalence of categories implied by the analytic localization method is not as strong as it could be. In this paper, a refinement of the Hecht-Taylor method, called equivariant analytic localization, is developed. The technical advantages that equivariant analytic localization has over (non-equivariant) analytic localization are discussed and applications are indicated.
Introduction Preliminaries The category ${/mathcal T}$ Two equivalences of categories The category $D^b_{G_0}({/mathcal D}_X)$ Descended structures The category $D^b_{G_0}({/mathcal U}_0(/mathfrak g))$ Localization Our main equivalence of categories Equivalence for any ergular weight $/lambda$ Bibliography.
| Erscheint lt. Verlag | 1.9.2001 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Zusatzinfo | bibliography |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 198 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-13 | 9780821827253 / 9780821827253 |
| Zustand | Neuware |
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