Representation Theory of the Symmetric Group

By V. Lakshmibai, J. Brown. 2009

595 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/e0efbf3cadf860a088524f1f98084d1c06d311a1

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In Discrete Mathematics and Combinatorics

In Electrical and Electronic Engineering

In Organic Chemistry

Citations in the corpus

Graded polynomial identities and exponential growth (2009, background): “From the hook formula giving the degree of an irreducible Sn-character (see [17]), we get that for j = 1, .”
Representations of Hecke Algebras at Roots of Unity (2011, unknown): “The simple C[6n]-modules are naturally parametrized by the partitions A t-n (see [33]).”
Quantum Conditional Mutual Information and Approximate Markov Chains (2014, background): “thonormal bases of VD,λ and VE,λ, respectively, with respect to which the representations of the symmetric group Sn are given by the same real-valued 24 matrices. (Such bases always exist, see, e.g., [31].) We then deﬁne the maximally entangled vector |ψλiV D,λVE,λ on VD,λ ⊗VE,λ by |ψλiV D,λVE,λ = r”
Graded polynomial identities and codimensions: computing the exponential growth (2010, methodology): “Now, by the branching theorem (see [15]), it follows that there exists a multipartition 〈μ〉 = (μ(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 orders of zeros of irreducible characters (2009, background): “We recall that if π is the partition of n corresponding to the character χ ∈ Irr(Sym(n)), then χAlt(n) is irreducible if and only if the Young diagram corresponding to the partition π is not symmetric (note that in [14] symmetric Young diagrams are called “self-associated”).”
On fixed points of permutations (2007, background): “2 of [47], there is the following useful description of conjugacy classes of G Sn where G is a finite group.”
ELEMENTARY PROOFS OF VARIOUS FACTS ABOUT 3-CORES (2009, unknown): “See James and Kerber [7] for a fuller discussion of the deﬁnition of t -cores.”
QUANTUM COHOMOLOGY AND THE k-SCHUR BASIS (2005, background): “, p−1, where zeros lie on the main diagonal (see [15] for more on cores and residues).”
Representations of the Infinite Symmetric Group (2016, background): “, CeccheriniSilberstein, Scarabotti, and Tolli [29], Fulton and Harris [42], James and Kerber [57], Simon [111], Vinberg [129], Zelevinsky [135].”