Skeins and quantum SU(N) invariants of 3-manifolds

Yokota, Yoshiyuki

doi:10.1007/s002080050025

Cited by 34 publications

(47 citation statements)

References 11 publications

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“…Remark It is known that quantum invariants of 3-manifolds can be constructed via linear skein theories based on the Kauffman bracket skein modules (see [255]) and the Homflypt skein modules [408].…”

Section: Problem 412 Construct Invariants Of 3-manifolds Via a Lineamentioning

confidence: 99%

Problems on invariants of knots and 3–manifolds

Ohtsuki¹

2004

Geometry &Amp; Topology Monographs

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Section: Problem 412 Construct Invariants Of 3-manifolds Via a Lineamentioning

confidence: 99%

Problems on invariants of knots and 3–manifolds

Ohtsuki¹

2004

Geometry &Amp; Topology Monographs

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“…The idea of the construction is to insert symmetrizers along rows and antisymmetrizers along columns, and then to normalize. A skein computation of the normalizing coefficient (of slightly different idempotents) appeared in [24]. Details about the construction of these idempotents can also be found in [5].…”

Section: Hecke Algebrasmentioning

confidence: 99%

“…λỹ(µ,ν)ŷλ (24) From the above formula we obtain a minimal idempotentỹ λ if the following three conditions are satisfied:…”

Section: Formulas For the Idempotents And The Non Generic Casementioning

confidence: 99%

Skein construction of idempotents in Birman-Murakami-Wenzl algebras

Beliakova¹,

Blanchet²

2001

Mathematische Annalen

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Abstract. We give skein theoretic formulas for minimal idempotents in the Birman-Murakami-Wenzl algebras. These formulas are then applied to derive various known results needed in the construction of quantum invariants and modular categories. In particular, an elementary proof of the Wenzl formula for quantum dimensions is given. This proof does not use the representation theory of quantum groups and the character formulas.

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“…We find that E is a non-zero element in C½S jDj by using the result in [16]. Therefore it is not difficult to check that the idempotent E is also a projection which is similar toÊ E .…”

Section: Young Symmetrizerê E Y D For Young Tableau Y Dmentioning

confidence: 90%

“…In fact, Yokota constructed the diagrammatic realization of the quantum modified Young symmetrizer in [16].…”

Section: Young Symmetrizerê E Y D For Young Tableau Y Dmentioning

confidence: 99%

A Diagrammatic Construction of the (sl(N,C),ρ)-Weight System

Nagasato

2003

IIS

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In this paper, we first give a diagrammatic analogue of the Young symmetrizer. By using this, the ðslðN; CÞ; Þ-weight system for an arbitrary finite-dimensional irreducible representation is formulated in a diagrammatic way. The formula is useful for the calculations of the ðslðN; CÞ; Þ-weight system in the sense that we do not need actual constructions of the representations of slðN; CÞ essentially. Hence by using this and the modified Kontsevich integral we can get the quantum ðslðN; CÞ; Þ-invariant for any finite-dimensional irreducible representation without actual constructions of the representations of slðN; CÞ. The diagrammatic construction is a generalization of the formula given in ''Remarks on the ðslðN; CÞ; adÞ-weight system''.

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Skeins and quantum SU(N) invariants of 3-manifolds

Cited by 34 publications

References 11 publications

Problems on invariants of knots and 3–manifolds

Problems on invariants of knots and 3–manifolds

Skein construction of idempotents in Birman-Murakami-Wenzl algebras

A Diagrammatic Construction of the (sl(N,C),ρ)-Weight System

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