Representations of quantum algebras and combinatorics of young tableaux
By 有木 進. 2002
97 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/c007004474109456f294c2ae2fd4e7586cea0584
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Citations in the corpus
- Crystals from categorified quantum groups (2009, methodology): “Ariki’s categorification theorem gave a geometric proof that the sum of complexified Grothendieck groups of cyclotomic Hecke algebras H m at an N -th root of unity over C, taken over all m 0, was isomorphic to the highest weight representation V (Λ) of U(ŝlN) [1], see [2,3,6,48] and also [16,40].”
- Derived equivalences and finite dimensional algebras (2006, unknown): “[4]).”
- 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].”
- Representation theory of symmetric groups and related Hecke algebras (2009, unknown): “(6) elements of a standard spanning set of V (Λ) coming from the construction of V (Λ) in terms of a higher level Fock space correspond to the classes of the Specht modules over cyclotomic Hecke algebras [5]; (7) provided F = C, elements of the dual canonical basis in V (Λ) correspond to the classes”
- Graded Specht modules (2009, methodology): “In the remainder of the article, we develop the theory of graded Specht modules more generally for cyclotomic Hecke algebras of arbitrary level as in [2].”
- Graded decomposition numbers for cyclotomic Hecke algebras (2009, background): “Now we proceed to introduce the higher level Fock space F (Λ) following the exposition in [A3].”
- On the parametrization of the simple modules for Ariki-Koike algebras at roots of unity (2003, methodology): “In particular, the crystal graph gives a way for labeling the KashiwaraLusztig’s canonical basis of M (see [4] for more details).”