Linear and Projective Representations of Symmetric Groups

By Alexander S. Kleshchev. 2005

304 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9aacdef0f137b159c7f3896f86423714be7857f6

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Mathematical Physics

Citations in the corpus

A categorification of quantum sl(n) (2008, unknown): “This 2-category or its mild modifications is expected to act on parabolic-singular blocks of highest weight categories for slN in the context of categorification of sln representations [7], [10], [31], on derived categories of coherent sheaves on Kronheimer–Nakajima [20] and Nakajima [26] quiver var”
Centers of degenerate cyclotomic Hecke algebras and parabolic category (2006, background): “We point out that F is a splitting field for the algebra Hµ d; one way to see this is to observe that the construction of the irreducible Hµ d-modules over the algebraic closure of F from [ K ,§5.4] already makes sense over F itself.”
Crystals from categorified quantum groups (2009, background): “Kleshchev’s book contains an excellent exposition of Grojnowski’s approach in the context of degenerate affine Hecke algebras [37].”
Representations of Lie superalgebras in prime characteristic I (2008, background): “... associative superalgebras over K are classified into two types: besides the usual matrix superalgebra (called type M ) there are in addition simple superalgebras of type Q. Alternatively, a superalgebra analog of Schur’s Lemma states that the endomorphism ring of an irreducible module of a super”
Highest weight categories arising from Khovanov's diagram algebra III: category O (2008, unknown): “1 by a general argument originating in [KL], sometimes known as Lusztig’s lemma; see e.”
Homogeneous representations of Khovanov-Lauda algebras (2008, methodology): “A module M ∈ R�-mod is called calibrated if y1,...,yd act as zero on M. Other authors might use different terminology here, for example Gelfand-Zetlin [Ch, OV], completely splittable [K1, K2 , Ru], skew [Mo], seminormal [Ma], etc.”
Representation theory of symmetric groups and related Hecke algebras (2009, unknown): “There is a more elementary approach to the classification of irreducible HΛ d modules based on the socle branching rules, see [81] and [125].”
Quiver Hecke Algebras and 2-Lie Algebras (2011, background): “We recall in this section some classical results on representations of symmetric groups and related Hecke algebras, and the relation with Fock spaces [1, 11, 18, 26].”
Graded Specht modules (2009, background): “All the results have analogues in the degenerate case as in [18], with the symmetric group picture described above being the degenerate case for level one.”
Schur–Weyl duality for higher levels (2006, methodology): “The map J! K ,(i,j)7! (row(i),row(j),col(j) col(i)) is a bijection.”
A diagrammatic approach to categorification of quantum groups II (2008, methodology): “Sur-jectivity of γ follows from the arguments identical to those given in [4, Section 3.2], which, in turn, were adopted from [5, Section 5].”
Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras (2008, methodology): “It is now very easy to check that the relations (1.6)‐(1.15) are satisfied, hence applying our Main Theorem in this very special case we get an H -action on S( ). Moreover, if S,T2 T ( ) then one can obtain T from S by a series of basic transpositions so that on each step we still have a standard ta”