Alan Huckleberry – författare & böcker

Cycle Spaces of Flag Domains

A Complex Geometric Viewpoint

Inbunden, Engelska, 2005

1 398 kr

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This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?ag domains. Some of the methods are now standard, but many are new. The exposition is carried out from the viewpoint of complex algebraic and differential geometry. Except for certain foundational material,whichisreadilyavailablefromstandardtexts,itisessentiallyself-contained; at points where this is not the case we give extensive references. After developing the background material on complex ?ag manifolds and rep- sentationtheory, wegiveanexposition(withanumberofnewresults)ofthecomplex geometric methods that lead to our characterizations of (group theoretically de?ned) cyclespacesandtoanumberofconsequences. Thenwegiveabriefindicationofjust how those results are related to the representation theory of semisimple Lie groups through, for example, the theory of double ?bration transforms, and we indicate the connection to the variation of Hodge structure. Finally, we work out detailed local descriptions of the relevant full Barlet cycle spaces. Cycle space theory is a basic chapter in complex analysis. Since the 1960s its importance has been underlined by its role in the geometry of ?ag domains, and by applications in the representation theory of semisimple Lie groups. This developed veryslowlyuntilafewofyearsagowhenmethodsofcomplexgeometry,inparticular those involving Schubert slices, Schubert domains, Iwasawa domains and suppo- ing hypersurfaces, were introduced. In the late 1990s, and continuing through early 2002, we developed those methods and used them to give a precise description of cycle spaces for ?ag domains. This effectively enabled the use of double ?bration transforms in all ?ag domain situations.

Cycle Spaces of Flag Domains

A Complex Geometric Viewpoint

AvJoseph A. Wolf,Alan Huckleberrym. fl.

E-bok

PDF, Engelska, 2006

1 733 kr

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This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?ag domains. Some of the methods are now standard, but many are new. The exposition is carried out from the viewpoint of complex algebraic and differential geometry. Except for certain foundational material,whichisreadilyavailablefromstandardtexts,itisessentiallyself-contained; at points where this is not the case we give extensive references. After developing the background material on complex ?ag manifolds and rep- sentationtheory, wegiveanexposition(withanumberofnewresults)ofthecomplex geometric methods that lead to our characterizations of (group theoretically de?ned) cyclespacesandtoanumberofconsequences. Thenwegiveabriefindicationofjust how those results are related to the representation theory of semisimple Lie groups through, for example, the theory of double ?bration transforms, and we indicate the connection to the variation of Hodge structure. Finally, we work out detailed local descriptions of the relevant full Barlet cycle spaces. Cycle space theory is a basic chapter in complex analysis. Since the 1960s its importance has been underlined by its role in the geometry of ?ag domains, and by applications in the representation theory of semisimple Lie groups. This developed veryslowlyuntilafewofyearsagowhenmethodsofcomplexgeometry,inparticular those involving Schubert slices, Schubert domains, Iwasawa domains and suppo- ing hypersurfaces, were introduced. In the late 1990s, and continuing through early 2002, we developed those methods and used them to give a precise description of cycle spaces for ?ag domains. This effectively enabled the use of double ?bration transforms in all ?ag domain situations.

Lie Groups: Structure, Actions, and Representations

In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday

AvAlan Huckleberry,Ivan Penkovm. fl.

Inbunden, Engelska, 2013

1 077 kr

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Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profound contributions to mathematics. Due to Professor Wolf’s broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods are employed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representation spaces are discussed. Contributions in the area of representation theory involve numerous viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. OshimaA. Andrada I. PacharoniM. L. Barberis F. RicciL. Barchini S. RosenbergI. Dotti N. ShimenoM. Eastwood J.TiraoV. Fischer S. TreneerT. Kobayashi C.T.C. WallA. Korányi D. WallaceB. Kostant K. WiboontonP. Kostelec F. XuK.-H. Neeb O. YakimovaG. Olafsson R. ZierauB. Ørsted

Lie Groups: Structure, Actions, and Representations

In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday

AvGregg Zuckerman,Ivan Penkovm. fl.

E-bok

PDF, Engelska, 2013

1 416 kr

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Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf''s profound contributions to mathematics. Due to Professor Wolf’s broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods are employed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representation spaces are discussed. Contributions in the area of representation theory involve numerous viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis.

Contributors

D. Akhiezer T. Oshima

A. Andrada I. Pacharoni

M. L. Barberis F. Ricci

L. Barchini S. Rosenberg

I. Dotti N. Shimeno

M. Eastwood J.Tirao

V. Fischer S. Treneer

T. Kobayashi C.T.C. Wall

A. Korányi D. Wallace

B. Kostant K. Wiboonton

P. Kostelec F. Xu

K.-H. Neeb O. Yakimova

G. Olafsson R. Zierau

B. Ørsted

Lie Groups: Structure, Actions, and Representations

In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday

AvAlan Huckleberry,Ivan Penkovm. fl.

Häftad, Engelska, 2015

1 077 kr

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Infinite Dimensional Kahler Manifolds

AvTilmann Wurzbacher,Alan Huckleberry

E-bok

PDF, Engelska, 2012

712 kr

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Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.

Global Aspects of Complex Geometry

AvFabrizio Catanese,Hélène Esnaultm. fl.

Inbunden, Engelska, 2006

1 077 kr

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This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry

Global Aspects of Complex Geometry

AvThomas Peternell,Klaus Hulekm. fl.

E-bok

PDF, Engelska, 2006

1 367 kr

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This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kähler geometry, and group actions to Hodge theory and characteristic p-geometry.

Written by established experts this book will be a must for mathematicians working in Complex Geometry

Global Aspects of Complex Geometry

AvFabrizio Catanese,Hélène Esnaultm. fl.

Häftad, Engelska, 2010

1 077 kr

Skickas inom 10-15 vardagar

This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry

Infinite Dimensional Kähler Manifolds

AvAlan Huckleberry,Tilmann Wurzbacher

Häftad, Engelska, 2001

542 kr

Skickas inom 10-15 vardagar

Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.

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Alan Huckleberry – författare

Cycle Spaces of Flag Domains

Cycle Spaces of Flag Domains

Lie Groups: Structure, Actions, and Representations

Lie Groups: Structure, Actions, and Representations

Lie Groups: Structure, Actions, and Representations

Infinite Dimensional Kahler Manifolds

Global Aspects of Complex Geometry

Global Aspects of Complex Geometry

Global Aspects of Complex Geometry

Infinite Dimensional Kähler Manifolds

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