Homogeneous representations of Khovanov-Lauda algebras

By Alexander S. Kleshchev, Arun Ram. 2008

71 citations recorded by the source corpus.

We construct irreducible graded representations of simply laced Khovanov�Lauda algebras which are concentrated in one degree. The underlying combinatorics of skew shapes and standard tableaux corresponding to arbitrary simply laced types has been developed previously by Peterson, Proctor and Stembridge. In particular, the Peterson�Proctor hook formula gives the dimensions of the homogeneous irreducible modules corresponding to straight shapes.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/055e2e364542ecce452137373ad666e7bac7f27b

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Citations in the corpus

Implicit structure in 2-representations of quantum groups (2011, background): “Z is the integral version of the irreducible highest weight representation for U(˙ g) associated to Λ and [Proj( RΛ)] is the Grothendieck ring of Proj( ). Parts of this conjecture have been proven in [4, 19, 3, 24, 20, 14]. Recently Kang and Kashiwara [13] prove this conjecture by showing that i-ind”
Homological properties of finite type Khovanov-Lauda-Rouquier algebras (2012, unknown): “ §3.2], and the word l(α) coincides with the word iα from (4.12). Proof. This follows by inspection of the data in the examples. Finally we recall the construction of homogeneous representations from [KR1]. Let ∼be the equivalence relation on hIigenerated by interchanging an adjacent pair of letters”
Crystals from categorified quantum groups (2009, background): “In type A homogeneous cellular bases were constructed [39,12,22].”
Representation theory of symmetric groups and related Hecke algebras (2009, unknown): “e ones in Theorem 4.1(i). Moreover, if our skew shape is a shape, there is a hook formula for any Lie type which computes the dimension of the corresponding irreducible module! We refer the reader to [127] for the details on that. On the other hand, non-pure irreducible modules are much harder to un”
Representations of Khovanov–Lauda–Rouquier algebras and combinatorics of Lyndon words (2009, background): “and only if j = sr i for some admissible transposition sr for i. Explicit combinatorial descriptions of the connected components of Gα can be found in [ 11 ].”