Jucys-Murphy elements and a presentation for partition algebras

We give a new presentation for the partition algebras. This presentation was discovered in the course of establishing an inductive formula for the partition algebra Jucys-Murphy elements defined by Halverson and Ram [European J. Combin. 26 (2005), 869-921]. Using Schur-Weyl duality we show that our recursive formula and the original definition of Jucys-Murphy elements given by Halverson and Ram are equivalent. The new presentation and inductive formula for the partition algebra Jucys-Murphy elements given in this paper are used to construct the seminormal representations for the partition algebras in a separate paper.Comment: 39 pages, 9 figures. Typos corrected and editorial changes made from v1-3. The final publication is available at springerlink.co

A seminormal form for partition algebras

Using a new presentation for partition algebras (J. Algebraic Combin. 37(3):401-454, 2013), we derive explicit combinatorial formulae for the seminormal representations of the partition algebras. These results generalise to the partition algebras the classical formulae given by Young for the symmetric group.Comment: Published version. 51 pages, includes figures and table

Specht modules and semisimplicity criteria for Brauer and Birman--Murakami--Wenzl Algebras

A construction of bases for cell modules of the Birman--Murakami--Wenzl (or B--M--W) algebra $B_n(q,r)$ by lifting bases for cell modules of $B_{n-1}(q,r)$ is given. By iterating this procedure, we produce cellular bases for B--M--W algebras on which a large abelian subalgebra, generated by elements which generalise the Jucys--Murphy elements from the representation theory of the Iwahori--Hecke algebra of the symmetric group, acts triangularly. The triangular action of this abelian subalgebra is used to provide explicit criteria, in terms of the defining parameters $q$ and $r$, for B--M--W algebras to be semisimple. The aforementioned constructions provide generalisations, to the algebras under consideration here, of certain results from the Specht module theory of the Iwahori--Hecke algebra of the symmetric group

Simple modules for the partition algebra and monotone convergence of Kronecker coefficients

We construct bases of the simple modules for partition algebras which are indexed by paths in an alcove geometry. This allows us to give a concrete interpretation (and new proof) of the monotone convergence property for Kronecker coefficients using stratifications of the cell modules of the partition algebra

Zeolite-cage-lock strategy for in situ synthesis of highly nitrogen-doped porous carbon for selective separation of carbon dioxide gas

Porous carbon structures doped with 18.14% nitrogen and prepared by a carbonizing organic template in ZSM-39 zeolitic cages show high CO2 adsorption capacity.</p

Unique allosteric effect driven rapid adsorption of carbon dioxide on a new ionogel [P4444][2-Op]@MCM-41 with excellent cyclic stability and loading-dependent capacity

Allosteric effect-driven rapid stepwise CO2 adsorption of pyridine-containing anion functionalized ionic liquid [P4444][2-Op] confined into mesoporous silica MCM-41.</p