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

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 algebr

Unequal Perylene Diimide Twins in a Quadruple Assembly

Natural light-harvesting (LH) systems can divide identical dyes into unequal aggregate states, thereby achieving intelligent "allocation of labor". From a synthetic point of view, the construction of such kinds of unequal and integrated systems without the help of proteinaceous scaffolding is challenging. Here, we show that four octatetrayne-bridged ortho-perylene diimide (PDI) dyads (POPs) self-assemble into a quadruple assembly (POP)4 both in solution and in the solid state. The two identical PDI units in each POP are compartmentalized into weakly coupled PDIs (P520) and closely stacked PDIs (P550) in (POP)4 . The two extreme pools of PDI chromophores were unambiguously confirmed by single-crystal X-ray crystallography and NMR spectroscopy. To interpret the formation of the discrete quadruple assembly, we also developed a two-step cooperative model. Quantum-chemical calculations indicate the existence of multiple couplings within and across P520 and P550, which can satisfactorily describe the photophysical properties of the unequal quadruple assembly. This finding is expected to help advance the rational design of dye stacks to emulate functions of natural LH systems.</p

The blocks of the partition algebra in positive characteristic

In this paper we describe the blocks of the partition algebra over a field of positive characteristic

Privatization and non-tradable stock reform in China: The case of Valin Steel Tube & Wire Co., Ltd.

While China had been vigorously pursuing economic reform since the late 1980s, it wasn't until the 2005-2006 time period that non-tradable stock reform took place. The case of Hunan Valin Steel provides a rich look inside about the dynamics of the non-tradable share reform in China, and demonstrates the impact of good financial design helping the company to turn aside the financial distress, while minimizing costs to benefit the stockholders. Moreover, this case provides an illustration of the challenges posed by agency problems in China, with conflicted interests between tradable shareholders (public investors) on one hand and non-tradable shareholders (governments and state-owned enterprises) on the other. Not only does the split share structure result in conflicted interests and asymmetric information between managers and owners, but it also made it difficult to establish effective corporate governance.Ownership structure Non-tradable stock reform Chinese equity market Split share structure