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Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products

Pavel Etingof, Wee Liang Gan, Victor Ginzburg, Alexei Oblomkov (2007)

Publications Mathématiques de l'IHÉS

The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...

Hecke-Clifford algebras and spin Hecke algebras. IV: Odd double affine type.

Khongsap, Ta, Wang, Weiqiang (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Higher dimensional algebra. VII: Groupoidification.

Baez, John C., Hoffnung, Alexander E., Walker, Christopher D. (2010)

Theory and Applications of Categories [electronic only]

Homfly polynomials of generalized Hopf links.

Morton, Hugh R., Hadji, Richard J. (2002)

Algebraic & Geometric Topology

Homogeneous representations of Khovanov–Lauda Algebras

Alexander Kleshchev, Arun Ram (2010)

Journal of the European Mathematical Society

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.