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7 papers · 1 filter
On the idempotents of Hecke algebras
A. P. Isaev, A. I. Molev, A. F. Os'kin
We give a new construction of primitive idempotents of the Hecke algebras associated with the symmetric groups. The idempotents are found as evaluated products of certain rational…
Symmetries and invariants of twisted quantum algebras and associated Poisson algebras
A. I. Molev, E. Ragoucy
We construct an action of the braid group B_N on the twisted quantized enveloping algebra U'_q(o_N) where the elements of B_N act as automorphisms. In the classical limit q -> 1 we…
Gauss Decomposition of the Yangian Y(gl_{m|n})
Lucy Gow
We describe a Gauss decomposition for the Yangian Y(gl_{m|n}) of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical…
Character and dimension formulae for general linear superalgebra
Yucai Su, R. B. Zhang
The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we e…
Quantum superalgebra representations on cohomology groups of non-commutative bundles
R. B. Zhang
Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant funct…
Yangians and their applications
A. I. Molev
This is a review paper on the algebraic structure and representations of the A type Yangian and the B, C, D types twisted Yangians. Some applications to constructions of Casimir el…