Centers and Azumaya loci of finite WW-algebras

In this paper, we study the center $Z$ of the finite $W$-algebra $\mathcal{T}(\mathfrak{g},e)$ associated with a semi-simple Lie algebra $\mathfrak{g}$ over an algebraically closed field \mathds{k} of characteristic $p\gg0$, and an arbitrarily given nilpotent element $e\in\mathfrak{g}$. We obtain an analogue of Veldkamp's theorem on the center. For the maximal spectrum $\text{Specm}(Z)$, we show that its Azumaya locus coincides with its smooth locus of smooth points. The former locus reflects irreducible representations of maximal dimension for $\mathcal{T}(\mathfrak{g},e)$.Comment: 31 page

A General Equilibrium Model of the Term Structure of Interest Rates under Regime-switching Risk

This paper incorporates the systematic risk of regime shifts into a general equilibrium model of the term structure of interest rates. The model shows that there is a new source of time-variation in bond term premiums in the presence of regime shifts. This new component is a regime-switching risk premium that depends on the covariations between discreet changes in marginal utility and bond prices across different regimes. A closed-form solution for the term structure of interest rates is obtained under an affine model using log-linear approximation. The model is estimated by Efficient Method of Moments. The regime-switching risk is found to be statistically significant and mostly affect the long-end of the yield curveThe Term Structure, General Equilibrium, Markov Regime Shifts

Super Vust theorem and Schur-Sergeev duality for principal finite WW-superalgebras

In this paper, we first formulate a super version of Vust theorem associated with a regular nilpotent element $e\in\mathfrak{gl}(V)$. As an application of this theorem, we then obtain the Schur-Sergeev duality for principal finite $W$-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality.Comment: 35 pages, comments are welcom