A new approach to representation theory of symmetric groups

Okounkov, Andreĭ; Vershik, A. M.

doi:10.1007/bf02433451

Cited by 207 publications

(221 citation statements)

References 9 publications

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“…To do this, one replaces the maximal torus with the subalgebra of the group algebra of the symmetric group generated by the Jucys-Murphy elements [OV, Section 2] X i , which is the sum of the transpositions (1, i) + (2, i) + · · · + (i − 1, i), and is well defined for the infinite symmetric group. The relevant character theory is explained in [OV,Section 5]. The punchline is that V d λ has a basis v T indexed by standard Young tableaux T of shape (d − |λ|, λ) which is an eigenbasis for X 2 , X 3 , .…”

Section: The Category Modmentioning

confidence: 99%

Stability Patterns in Representation Theory

Sam

Snowden

2015

Forum math. Sigma

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We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is an array of equivalences between the stable representation category and various other categories, each of which has its own flavor (representation theoretic, combinatorial, commutative algebraic, or categorical) and offers a distinct perspective on the stable category. We use this theory to produce a host of specific results: for example, the construction of injective resolutions of simple objects, duality between the orthogonal and symplectic theories, and a canonical derived auto-equivalence of the general linear theory.

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Section: The Category Modmentioning

confidence: 99%

Stability Patterns in Representation Theory

Sam

Snowden

2015

Forum math. Sigma

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“…This follows from the known values of the simultaneous eigenvalues of the Jucys-Murphy elements s k,k+1 + s k,k+2 + · · · + s k,n used to defined τ c . See for example [OV,Theorem 5.8]. Proof.…”

Section: Nonzero Dirac Cohomology For Type Amentioning

confidence: 99%

Unitary Hecke algebra modules with nonzero Dirac cohomology

Barbasch

Ciubotaru

2014

Symmetry: Representation Theory and Its Applications

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“…This construction could be regarded as a cellular analogue of the constructions in [34][35][36]38]. Each of the examples that we want to study is a tower (A n ) n≥0 of algebras that generically is obtained from another tower (Q n ) n≥0 by repeated Jones basic constructions.…”

Section: Introductionmentioning

confidence: 99%