Let S(Λ) be the cyclotomic q-Schur algebra associated to the ArikiKoike algebra H . We construct a certain subalgebra S(Λ) of S(Λ), and show that it is a standardly based algebra in the sense of Du and Rui. S(Λ) has a natural quotient S(Λ), which turns out to be a cellular algebra. In the case where the modified Ariki-Koike algebra H ♭ is defined, S(Λ) coincides with the cyclotomic q-Schur alge...

We investigate the spectral geometry of the exceptional Jordan algebra and its extensions. We examine the spectrum of the exceptional Jordan algebra over the sixteen-dimensional space of primitive idempotents, where it exhibits three real eigenvalues. We interpret the spectrum as coordinates for a coincident D-brane system where the real eigenvalues correspond to positions of three D0-branes on...

This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinitedimensional Lie algebras of quantum matrix models, one for the open string sector and one for the closed string sector. Physical observables of quantum matrix models in the large-N limit can be expressed as elements of these Lie algebras. We wil...

We describe the quasitriangular structure (universal R-matrix) on the non-standard quantum group U q (H 1 , H 2 , X ±) associated to the Alexander-Conway matrix solution of the Yang-Baxter equation. We show that this Hopf algebra is connected with the super-Hopf algebra U q gl (1|1) by a general process of superization.