Equivariant Analytic Localization of Group Representations
Title | Equivariant Analytic Localization of Group Representations PDF eBook |
Author | Laura Ann Smithies |
Publisher | American Mathematical Soc. |
Pages | 106 |
Release | 2001 |
Genre | Mathematics |
ISBN | 0821827251 |
This book is intended for graduate students and research mathematicians interested in topological groups, Lie groups, category theory, and homological algebra.
Homotopy Theory of Diagrams
Title | Homotopy Theory of Diagrams PDF eBook |
Author | Wojciech Chachólski |
Publisher | American Mathematical Soc. |
Pages | 106 |
Release | 2002 |
Genre | Mathematics |
ISBN | 0821827596 |
In this paper the authors develop homotopy theoretical methods for studying diagrams. In particular they explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept introduced is that of a model approximation. A model approximation of a category $\mathcal{C}$ with a given class of weak equivalences is a model category $\mathcal{M}$ together with a pair of adjoint functors $\mathcal{M} \rightleftarrows \mathcal{C}$ which satisfy certain properties. The key result says that if $\mathcal{C}$ admits a model approximation then so does the functor category $Fun(I, \mathcal{C})$.
The Submanifold Geometries Associated to Grassmannian Systems
Title | The Submanifold Geometries Associated to Grassmannian Systems PDF eBook |
Author | Martina Brück |
Publisher | American Mathematical Soc. |
Pages | 111 |
Release | 2002 |
Genre | Mathematics |
ISBN | 0821827537 |
This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.
Blowing Up of Non-Commutative Smooth Surfaces
Title | Blowing Up of Non-Commutative Smooth Surfaces PDF eBook |
Author | M. van den Bergh |
Publisher | American Mathematical Soc. |
Pages | 157 |
Release | 2001 |
Genre | Mathematics |
ISBN | 0821827545 |
This book is intended for graduate students and research mathematicians interested in associative rings and algebras, and noncommutative geometry.
Extending Intersection Homology Type Invariants to Non-Witt Spaces
Title | Extending Intersection Homology Type Invariants to Non-Witt Spaces PDF eBook |
Author | Markus Banagl |
Publisher | American Mathematical Soc. |
Pages | 101 |
Release | 2002 |
Genre | Mathematics |
ISBN | 0821829882 |
Intersection homology theory provides a way to obtain generalized Poincare duality, as well as a signature and characteristic classes, for singular spaces. For this to work, one has had to assume however that the space satisfies the so-called Witt condition. We extend this approach to constructing invariants to spaces more general than Witt spaces.
Generalized Whittaker Functions on $SU(2,2)$ with Respect to the Siegel Parabolic Subgroup
Title | Generalized Whittaker Functions on $SU(2,2)$ with Respect to the Siegel Parabolic Subgroup PDF eBook |
Author | Yasuro Gon |
Publisher | American Mathematical Soc. |
Pages | 130 |
Release | 2002 |
Genre | Mathematics |
ISBN | 0821827634 |
Obtains an explicit formula for generalized Whittaker functions and multiplicity one theorem for all discrete series representations of $SU(2,2)$.
Kac Algebras Arising from Composition of Subfactors: General Theory and Classification
Title | Kac Algebras Arising from Composition of Subfactors: General Theory and Classification PDF eBook |
Author | Masaki Izumi |
Publisher | American Mathematical Soc. |
Pages | 215 |
Release | 2002 |
Genre | Mathematics |
ISBN | 0821829351 |
This title deals with a map $\alpha$ from a finite group $G$ into the automorphism group $Aut({\mathcal L})$ of a factor ${\mathcal L}$ satisfying (i) $G=N \rtimes H$ is a semi-direct product, (ii) the induced map $g \in G \to [\alpha_g] \in Out({\mathcal L})=Aut({\mathcal L})/Int({\mathcal L})$ is an injective homomorphism, and (iii) the restrictions $\alpha \! \! \mid_N, \alpha \! \! \mid_H$ are genuine actions of the subgroups on the factor ${\mathcal L}$. The pair ${\mathcal M}={\mathcal L} \rtimes_{\alpha} H \supseteq {\mathcal N}={\mathcal L} DEGREES{\alpha\mid_N}$ (of the crossed product ${\mathcal L} \rtimes_{\alpha} H$ and the fixed-point algebra ${\mathcal L} DEGREES{\alpha\mid_N}$) gives an irreducible inclusion of factors with Jones index $\# G$. The inclusion ${\mathcal M} \supseteq {\mathcal N}$ is of depth $2$ and hence known to correspond to a Kac algebra of dim