122 research outputs found
Yang's system of particles and Hecke algebras
Contains fulltext :
104000.pdf (publisher's version ) (Open Access)35 p
Extensions of tempered representations
Let be irreducible tempered representations of an affine Hecke
algebra H with positive parameters. We compute the higher extension groups
explicitly in terms of the representations of analytic
R-groups corresponding to and . The result has immediate
applications to the computation of the Euler-Poincar\'e pairing ,
the alternating sum of the dimensions of the Ext-groups. The resulting formula
for is equal to Arthur's formula for the elliptic pairing of
tempered characters in the setting of reductive p-adic groups. Our proof
applies equally well to affine Hecke algebras and to reductive groups over
non-archimedean local fields of arbitrary characteristic. This sheds new light
on the formula of Arthur and gives a new proof of Kazhdan's orthogonality
conjecture for the Euler-Poincar\'e pairing of admissible characters.Comment: This paper grew out of "A formula of Arthur and affine Hecke
algebras" (arXiv:1011.0679). In the second version some minor points were
improve
Leo Strauss's Recovery of the Political: The City and Man as a reply to Carl Schmitt's The Concept of the Political
This dissertation demonstrates that Leo Strauss, in The City and Man, continues his response to Carl Schmitt�s arguments concerning the affirmation of the political, as outlined by Strauss in his 1932 article on Schmitt�s The Concept of the Political. In affirming the political, Strauss spoke of the 'theologico-political problem', or the question regarding who, or what, should rule society. Strauss outlines six criteria in his 1932 'Comments', which he argues can be found in Schmitt�s The Concept of the Political, as essential for the recovery of the political. In raising the question of the political, both Schmitt and Strauss return to the fundamental question regarding how one should live. In so doing, Strauss rejects Schmitt�s reliance on conflicting faiths and returns to the Socratic description of the best regime (politeia), understood as the best way of life, that is devoted to contemplation, peace and justice. In his argument in The City and Man, Strauss satisfies the six criteria outlined in his 'Comments': (1) the acceptance of moral evil within human nature; (2) the problem of opposition among groups; (3) the possibility of a non-neutral, transprivate obligation; (4) the need for a content that determines the distinction between friend and enemy; (5) a content that leads to a quarrel over the question of 'what is Right?' and (6) that the political must address 'the order of human things from a pure and whole knowledge'. This thesis demonstrates that Strauss�s 1964 book, The City and Man, indirectly addresses Schmitt�s general criteria, using an interpretation of Thucydides�s, Aristotle�s and Plato�s best regime � which is linked to the pursuit of wisdom, or the philosophic life � to provide a transpolitical standard that opposes Schmitt�s insistence on 'concrete' experience, that relies on historical destiny, and faith, as the guide to political life
A class of Calogero type reductions of free motion on a simple Lie group
The reductions of the free geodesic motion on a non-compact simple Lie group
G based on the symmetry given by left- and right
multiplications for a maximal compact subgroup are
investigated. At generic values of the momentum map this leads to (new) spin
Calogero type models. At some special values the `spin' degrees of freedom are
absent and we obtain the standard Sutherland model with three
independent coupling constants from SU(n+1,n) and from SU(n,n). This
generalization of the Olshanetsky-Perelomov derivation of the model with
two independent coupling constants from the geodesics on with
G=SU(n+1,n) relies on fixing the right-handed momentum to a non-zero character
of . The reductions considered permit further generalizations and work at
the quantized level, too, for non-compact as well as for compact G.Comment: shortened to 13 pages in v2 on request of Lett. Math. Phys. and
corrected some spelling error
Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by
certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of
the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is
invariant under the action of certain differential operators which include half
the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit
clusters of size at most k: they vanish when k+1 of their variables are
identified, and they do not vanish when only k of them are identified. We
generalize most of these properties to superspace using orthogonal
eigenfunctions of the supersymmetric extension of the trigonometric
Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular,
we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at
\alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span
an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N
commuting variables and N anticommuting variables. We prove that the ideal
{\mathcal I}^{(k,r)}_N is stable with respect to the action of the
negative-half of the super-Virasoro algebra. In addition, we show that the Jack
superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting
variables are equal, and conjecture that they do not vanish when only k of them
are identified. This allows us to conclude that the standard Jack polynomials
with prescribed symmetry should satisfy similar clustering properties. Finally,
we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for
the subspace of symmetric superpolynomials in N variables that vanish when k+1
commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we
present exceptions to an often made statement concerning the clustering
property of the ordinary Jack polynomials for (k,r,N)-admissible partitions
(see Footnote 2); 2) Conjecture 14 is substantiated with the extensive
computational evidence presented in the new appendix C; 3) the various tests
supporting Conjecture 16 are reporte
Logarithmic and complex constant term identities
In recent work on the representation theory of vertex algebras related to the
Virasoro minimal models M(2,p), Adamovic and Milas discovered logarithmic
analogues of (special cases of) the famous Dyson and Morris constant term
identities. In this paper we show how the identities of Adamovic and Milas
arise naturally by differentiating as-yet-conjectural complex analogues of the
constant term identities of Dyson and Morris. We also discuss the existence of
complex and logarithmic constant term identities for arbitrary root systems,
and in particular prove complex and logarithmic constant term identities for
the root system G_2.Comment: 26 page
Yang's system of particles and Hecke algebras (vol 145, pg 139, 1997)
Contains fulltext :
29473.pdf (preprint version ) (Open Access
Yang's system of particles and Hecke algebras
Contains fulltext :
29472.pdf (preprint version ) (Open Access
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