The weighted universal Coxeter group and some related conjectures of Lusztig

the evaluation of language related engagment and task related engagment with the purpose of investigating the effect of metatalk and task typology

abstract while task-based instruction is considered as the most effective way to learn a language in the related literature, it is oversimplified on various grounds. different variables may affect how students are engaged with not only the language but also with the task itself. the present study was conducted to investigate language and task related engagement on the basis of the task typolog...

Perverse Sheaves and the Kazhdan-lusztig Conjectures

Coxeter Elements and Kazhdan-lusztig Cells

By the correspondence between Coxeter elements of a Coxeter system (W, S, Γ) and the acyclic orientations of the Coxeter graph Γ, we study some properties of elements in the set C0(W ). We show that when W is of finite, affine or hyperbolic type, any w ∈ C0(W ) satisfies w ∼ LR wJ with `(wJ ) = |J | = m(w) for some J ⊂ S. Now assume that W is of finite or affine type. We give an explicit descri...

Coxeter groups: statistics and Kazhdan–Lusztig polynomials

Brundan-kazhdan-lusztig and Super Duality Conjectures

We formulate a general super duality conjecture on connections between parabolic categories O of modules over Lie superalgebras and Lie algebras of type A, based on a Fock space formalism of their Kazhdan-Lusztig theories which was initiated by Brundan. We show that the Brundan-Kazhdan-Lusztig (BKL) polynomials for gl(m|n) in our parabolic setup can be identified with the usual parabolic Kazhda...