Representations of the generalized symmetric groups.
Restricted Boolean group rings
In this paper we study restricted Boolean rings and group rings. A ring is if every proper homomorphic image of is boolean. Our main aim is to characterize restricted Boolean group rings. A complete characterization of non-prime restricted Boolean group rings has been obtained. Also in case of prime group rings necessary conditions have been obtained for a group ring to be restricted Boolean. A counterexample is given to show that these conditions are not sufficient.
Results related to Huppert’s - conjecture
We improve a few results related to Huppert’s - conjecture. We also generalize a result about the covering number of character degrees to arbitrary finite groups.
Revisiting the symmetries of the quantum Smorodinsky-Winternitz system in dimensions.
Right closing almost conjugacy for G-shifts of finite type
A G-shift of finite type (G-SFT) is a shift of finite type which commutes with the continuous action of a finite group G. For irreducible G-SFTs we classify right closing almost conjugacy, answering a question of Bill Parry.
Ring-theoretic properties of Iwasawa algebras: a survey.
Robinson-Schensted correspondence for the signed Brauer algebras.
R-S correspondence for and Klein-4 diagram algebras.
RSK bases and Kazhdan-Lusztig cells
From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, “ RSK bases” are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra. Applications to invariant theory, over various base rings, of the general linear group and representation theory, both ordinary and modular, of the symmetric group are discussed.