79 citations · 807 across the 61 of their papers we have counts for
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Jucys-Murphy elements for Birman-Murakami-Wenzl algebras
A. P. Isaev, O. V. Ogievetsky
The Birman-Wenzl-Murakami algebra, considered as the quotient of the braid group algebra, possesses the commutative set of Jucys--Murphy elements. We show that the set of Jucys--Mu…
Representations of A-type Hecke algebras
A. P. Isaev, O. Ogievetsky
We review some facts about the representation theory of the Hecke algebra. We adapt for the Hecke algebra case the approach of Okounkov and Vershik which was developed for the repr…
Braids, Shuffles and Symmetrizers
A. P. Isaev, O. V. Ogievetsky
Multiplicative analogues of the shuffle elements of the braid group rings are introduced; in local representations they give rise to certain graded associative algebras (b-shuffle…
Spectral extension of the quantum group cotangent bundle
A. Isaev, P. Pyatov
The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the a…
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…
On R-matrix representations of Birman-Murakami-Wenzl algebras
A. P. Isaev, O. V. Ogievetsky, P. N. Pyatov
We show that to every local representation of the Birman-Murakami-Wenzl algebra defined by a skew-invertible R-matrix one can associate pairings $V\otimes V\…
Cayley-Hamilton-Newton identities and quasitriangular Hopf algebras
A. P. Isaev, O. V. Ogievetsky, P. N. Pyatov
In the framework of the Drinfeld theory of twists in Hopf algebras we construct quantum matrix algebras which generalize the Reflection Equation and the RTT algebras. Finite-dimens…