Representations Of Infinite-dimensional And Braid Groups: Ergodicity, Irreducibility, And Linearity
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A01=Alexander Kosyak
Author_Alexander Kosyak
Braid Groups Bn
Category=PBG
Category=PBKF
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
forthcoming
Generalized Characteristic Polynomials
Haar Measure
Irreducible Representations
Ismagilov's Conjecture
LawrenceAcAEURA"Krammer Representations
Linearity Problem for Braid Groups
q-Natural Numbers
q-Pascal Triangle
Quasi-Invariant Measures on Infinite-Dimensional Spaces
Reduced Burau Representation
Unitary Representations of Infinite-Dimensional Lie Groups
Von Neumann Algebras
Product details
- ISBN 9781800619258
- Publication Date: 12 Jul 2026
- Publisher: World Scientific Europe Ltd
- Publication City/Country: GB
- Product Form: Hardback
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This book offers a systematic study of one particular representation of infinite-dimensional and braid groups, with a focus on the intricate relationships between ergodicity, irreducibility, and linearity. It develops a unified analytical framework for understanding how von Neumann algebras, quasi-invariant measures, and probabilistic methods interact in the representation theory of non-locally-compact groups, where classical tools such as Haar measure are not available.The first part of the book investigates representations of infinite-dimensional groups, including GL0 (2∞,ℝ), using operator-algebraic and measure-theoretic techniques to establish conditions for irreducibility. By connecting ergodic theory with algebraic structures, the author introduces new methods for constructing and analyzing representations that capture the complex symmetries of infinite-dimensional systems.The second part focuses on the representation theory of braid groups Bn, addressing the celebrated problem of linearity. It clarifies the relationship between the Lawrence-Krammer and reduced Burau representations and demonstrates that the Lawrence-Krammer representation can be viewed as a quantization of the symmetric square of the reduced Burau representation. This conceptual link reveals deep connections between braid group theory, quantum symmetries, and mathematical physics, offering fresh insights into one of the most dynamic areas of modern representation theory.
