Titlebook: Braid Groups; Christian Kassel,Vladimir Turaev Textbook 2008 Springer-Verlag New York 2008 Burau.Garside.Homotopy.Iwahori-Hecke.Markov.Per

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,Representations of the Iwahori–Hecke Algebras,dimensional representations over an algebraically closed field of characteristic zero in terms of partitions and Young diagrams. As an application, we prove that the reduced Burau representation introduced in Section 3.3 is irreducible. We end the chapter by a discussion of the Temperley–Lieb algebras.

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Garside Monoids and Braid Monoids,oids. In this chapter we investigate properties of monoids and specifically of Garside monoids. As an application, we give a solution of the conjugacy problem in the braid groups. We also discuss generalized braid groups associated with Coxeter matrices.

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GLIDE

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Fluctuation Theory for Lévy Processesbtained from the punctured disks by functorial constructions. We discuss here two such constructions and study the resulting linear representations of the braid groups: the Burau representation (Sections 3.1–3.3) and the Lawrence–Krammer–Bigelow representation (Sections 3.5–3.7). As an application o

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Basic Results on Lévy Processesalgebra of .. depending on two parameters . and .. Our interest in the Iwahori—Hecke algebras is due to their connections to braids and links and to their beautiful representation theory discussed in the next chapter.

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Fluctuation Theory for Lévy Processesdimensional representations over an algebraically closed field of characteristic zero in terms of partitions and Young diagrams. As an application, we prove that the reduced Burau representation introduced in Section 3.3 is irreducible. We end the chapter by a discussion of the Temperley–Lieb algebr

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,Lévy Processes and Their Characteristics,oids. In this chapter we investigate properties of monoids and specifically of Garside monoids. As an application, we give a solution of the conjugacy problem in the braid groups. We also discuss generalized braid groups associated with Coxeter matrices.

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