Unipotent Ideals and Harish-Chandra Bimodules by Ivan Loseu
A groundbreaking book that applies new geometric tools to one of the oldest problems in representation theory, expanding the field and paving the way for further progress
In the 1920s, Hermann Weyl gave a complete classification of the irreducible unitary representations of a compact Lie group G. Around the same time, Fritz Peter and Weyl showed that these irreducible unitary representations are fundamental objects for harmonic analysis on G. If G is instead a noncompact Lie group, such as GL_n(R), the classification of the irreducible unitary G-representations is a much more difficult problem, one that remains open in general. An idea, with its origins in the work of Kostant, Kirillov, and Vogan, is that the set of irreducible unitary G-representations should contain a finite set of “building blocks,” called unipotent representations, related to the set of nilpotent co-adjoint G-orbits. This book proposes a definition and theory of unipotent representations in the case of when G is a complex reductive Lie group, such as GL_n(C).
This definition is based on the theory of quantizations of symplectic singularities, especially the geometry of nilpotent co-adjoint orbits and their equivariant covers. The main theorems include a geometric classification of unipotent representations, a calculation of their infinitesimal characters, and a proof of their unitarity in the case of classical groups. Although further obstacles remain, this work paves the way for a general theory of unipotent representations of reductive Lie groups, which should in turn form the basis of the classification of irreducible unitary representations.
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The Girth Ramsey Theorem
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Riemann Surfaces and Related Topics
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Seminar on the Atiyah-Singer Index Theorem
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Lectures on Curves on an Algebraic Surface
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Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik
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The Einstein-Klein-Gordon Coupled System
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A Hierarchy of Turing Degrees
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Elementary Differential Topology
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An Introduction to G-Functions
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Some Problems of Unlikely Intersections in Arithmetic and Geometry
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The Norm Residue Theorem in Motivic Cohomology
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The Structure of Groups with a Quasiconvex Hierarchy
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Curvature and Betti Numbers
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Period Spaces for p-divisible Groups
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Exponential Sums and Differential Equations
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Functional Operators, Volume 2
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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom
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The Decomposition of Global Conformal Invariants
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Weyl Group Multiple Dirichlet Series
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Green's Function Estimates for Lattice Schroedinger Operators and Applications. (AM-158)
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Automata Studies
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Arithmetic and Geometry
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Stationary Processes and Prediction Theory
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Seminar on Singularities of Solutions of Linear Partial Differential Equations
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Contributions to Fourier Analysis
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Hoelder Continuous Euler Flows in Three Dimensions with Compact Support in Time
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Non-Archimedean Tame Topology and Stably Dominated Types
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The p-adic Simpson Correspondence
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The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures
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Contributions to the Theory of Games, Volume IV
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Seminar on Micro-Local Analysis
| SKU | Unavailable |
| ISBN 13 | 9780691294490 |
| ISBN 10 | 0691294496 |
| Title | Unipotent Ideals and Harish-Chandra Bimodules |
| Author | Ivan Loseu Dmytro Matvieievskyi Lucas Mason-Brown |
| Series | Annals Of Mathematics Studies |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Princeton University Press |
| Year published | 2027-01-12 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |