On the Representation Theory of the Symmetric Groups

By P. Py. 2005

711 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9febbf5211685680f69320815fcf759e53e059f7

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Universal graded Specht modules for cyclotomic Hecke algebras (2011, background): “Accidentally, what we call a column Specht module Sλ is what was called a Specht module in James’ book [13].”
Lengths of monotone subsequences in a Mallows permutation (2013, background): “This bijection is intimately related to the representation theory of the symm etric group [20, 12], the theory of symmetric functions [28], and the theory of partitions [3].”
Introduction to twisted commutative algebras (2012, background): “ant for us, we point the reader to [Ful, §7] (a more in-depth treatment of symmetric group representations over arbitrary rings can be found INTRODUCTION TO TWISTED COMMUTATIVE ALGEBRAS 9 in the book [Jam]). These constructions imply that the complex representations of Sn are all realizable over the”
Graded Specht modules (2009, methodology): “We begin by reviewing the Dipper-James-Mathas theory of Specht modules for HΛd , cf. [DJM, JM].”
Centers of degenerate cyclotomic Hecke algebras and parabolic category (2006, background): “hr(I)hs( J ) = hr(i1,...,ia,k1)h0(k1,k2)···h0(kc 1,kc)”
Representation theory of symmetric groups and related Hecke algebras (2009, neutral): “In level 1 this has been done by James [91] for ξ = 1 and Dipper and James [53] for ξ 6= 1.”
Group theoretical methods in machine learning (2008, background): “Some of the most comprehensive texts on the symmetric group, where many of the following results were taken from are [James, 1978],[James and Kerber, 1981] and [Sagan, 2001].”
On the blocks of the walled Brauer algebra (2007, background): “We will need some basic facts about symmetric group representations; details can be found in [Jam78].”
Stability in the homology of congruence subgroups (2012, methodology): “13] has Sμ ,μ(F) (though actually, the field F is not specified in the notation in [15]).”
Symmetric groups and expander graphs (2005, background): “The irreducible representations of the symmetric group Sym(N) are parameterized by the partitions λ of N. Almost the same is true the representations of the alternating group, but the correspondence in this case is not 1-to-1, see [ 11 , 13].”
Integrals of ψ-classes over double ramification cycles (2012, methodology): “This proposition is a reformulation of the Murnaghan-Nakayama rule [6].”
Heisenberg algebra and a graphical calculus (2010, background): “Okounkov and Vershik [35], [36] presented a detailed derivation of the basic representation theory of the symmetric group via these elements, see also [25, Chapter 2], [8, 13].”
Surveys in Combinatorics 2011: The cyclic sieving phenomenon: a survey (2010, background): “Readers interested in more information about representation theory, especially as it relates to symmetric groups, can consult the texts of James [35], James and Kerber [34], or Sagan [65].”
Advanced Determinant Calculus: A Complement (2005, background): “” For all undefined notation, I refer the reader to standard texts on the representation theory of symmetric groups, as for example [82, 83, 146].”