We show that an arbitrary Hankel matrix of a nite rank admits a Vandermonde decomposition: H = V T DV , where V is a con-uent Vandermonde matrix and D is a block diagonal matrix. This result was rst derived by Vandevoorde; our contribution here is a presentation that uses only linear algebra, speciically, the Jordan canonical form. We discuss the choices for computing this decomposition in only...

Let G be a real connected semisimple Lie group. For each v′, v, g ∈ G, we prove that lim m→∞ [a(vgv)] = s · b(g), where a(g) denotes the a-component in the Iwasawa decomposition of g = kan and b(g) ∈ A+ denotes the unique element that conjugate to the hyperbolic component in the complete multiplicative Jordan decomposition of g = ehu. The element s in the Weyl group of (G, A) is determined by y...

Let A be a symmetrizable generalized Cartan matrix. Let g be the corresponding Kac-Moody algebra. Let G(R) be Tits’ Kac-Moody group functor over commutative rings R associated to g. Then G(R) is given by five axioms KMG1-KMG5 which are natural extensions of the properties of Chevalley-Demazure group schemes. We give a construction of the Tits functor for symmetrizable Kac-Moody groups G using i...

We investigate the convergence of GMRES for an n by n Jordan block J . For each k that divides n we derive the exact form of the kth ideal GMRES polynomial and prove the equality max ‖v‖=1 min p∈πk ‖p(J)v‖ = min p∈πk max ‖v‖=1 ‖p(J)v‖, where πk denotes the set of polynomials of degree at most k and with value one at the origin, and ‖ · ‖ denotes the Euclidean norm. In other words, we show that ...

We consider the Fourier expansions of automorphic forms on general Lie groups, with a particular emphasis on exceptional groups. After describing some principles underlying known results on GL(n), Sp(4), and G2, we perform an analysis of the expansions on split real forms of E6 and E7 where simplifications take place for automorphic realizations of real representations which have small Gelfand-...

This paper is devoted to the study of the surjective stability of the K -functor for 1 Chevalley groups of type E . This is a particular case of the stability problem for 7 Chevalley groups, which was posed by H. Bass. In this paper, surjective stability of the K -functor is proved under natural conditions on the dimension of the maximal 1 spectrum of a ring and, independently, under a special ...

Jeffrey Adams, University of Maryland. The Chevalley Involution for Real Groups, with applications to the Fubini-Schur Indicator. The Chevalley involution of a complex group is unique up to conjugation, and takes any algebraic representation to its contragredient. The analogue over local fields is subtle. We prove that the Chevalley involution is defined over R, and with an appropriate conditio...