$q$-Krawtchouk polynomials as spherical functions on the Hecke algebra of type $B$

We give presentations, by means of diagrammatic generators and relations, of the analogues of the Temperley–Lieb algebras associated as Hecke algebra quotients to Coxeter graphs of type B and D. This generalizes Kauffman's diagram calculus for the Temperley–Lieb algebra.

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Unipotent Orbital Integrals of Hecke Functions for GL(n)

Canadian Journal of Mathematics ◽

10.4153/cjm-1994-015-3 ◽

1994 ◽

Vol 46 (2) ◽

pp. 308-323

Author(s):

Rebecca A. Herb

Keyword(s):

Linear Functional ◽

Elementary Proof ◽

Hecke Algebra ◽

Conjugacy Classes ◽

Spherical Functions ◽

Orbital Integrals ◽

Orbital Integral ◽

Linearly Independent ◽

Complete Set

AbstractLet G = GL(n, F) where F is a p-adic field, and let 𝓗(G) denote the Hecke algebra of spherical functions on G. Let u1,..., up denote a complete set of representatives for the unipotent conjugacy classes in G. For each 1 ≤ i ≤ p, let μi be the linear functional on such that μi(f) is the orbital integral of f over the orbit of ui. Waldspurger proved that the μi, 1 ≤ i ≤ p, are linearly independent. In this paper we give an elementary proof of Waldspurger's theorem which provides concrete information about the Hecke functions needed to separate orbits. We also prove a twisted version of Waldspurger's theorem and discuss the consequences for SL(n, F).

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Parameters for generalized Hecke algebras in type B

Journal of Algebra and Its Applications ◽

10.1142/s0219498819501731 ◽

2019 ◽

Vol 18 (09) ◽

pp. 1950173

Author(s):

Max Murin ◽

Seth Shelley-Abrahamson

Keyword(s):

Recent Work ◽

Parabolic Subgroup ◽

Coxeter Group ◽

Hecke Algebras ◽

Hecke Algebra ◽

Irreducible Representations ◽

Type B ◽

Full Support

The irreducible representations of full support in the rational Cherednik category [Formula: see text] attached to a Coxeter group [Formula: see text] are in bijection with the irreducible representations of an associated Iwahori–Hecke algebra. Recent work has shown that the irreducible representations in [Formula: see text] of arbitrary given support are similarly governed by certain generalized Hecke algebras. In this paper, we compute the parameters for these generalized Hecke algebras in the remaining previously unknown cases, corresponding to the parabolic subgroup [Formula: see text] in [Formula: see text] for [Formula: see text] and [Formula: see text].

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Biological and Morphological Studies on Low-Leukemia-Strain Mice with Hodgkin's-Like Neoplasia Induced by Serial Cell-Free Transmission of Leukemic Organs of SJL/J Strain Mice

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100100792 ◽

1968 ◽

Vol 26 ◽

pp. 210-211

Author(s):

S. Fujinaga ◽

K. Maruyama ◽

C.W. Williams ◽

K. Sekhri ◽

L. Dmochowski

Keyword(s):

Tissue Culture ◽

Type A ◽

Reticulum Cell ◽

Type B ◽

Viral Origin ◽

Serial Transfer ◽

Strain Mouse ◽

Morphological Studies ◽

Cell Neoplasm ◽

Free Material

Yumoto and Dmochowski (Cancer Res.27, 2098 (1967)) reported the presence of mature and immature type C leukemia virus particles in leukemic organs and tissues such as lymph nodes, spleen, thymus, liver, and kidneys of SJL/J strain mice with Hodgki's-like disease or reticulum cell neoplasm (type B). In an attempt to ascertain the possibility that this neoplasia may be of viral origin, experiments with induction and transmission of this neoplasm were carried out using cell-free extracts of leukemic organs from an SJL/J strain mouse with spontaneous disease.It has been possible to induce the disease in low-leukemia BALB/c and C3HZB strain mice and serially transfer the neoplasia by cell-free extracts of leukemic organs of these mice. Histological examination revealed the neoplasia to be of either reticulum cell-type A or type B. Serial transfer is now in its fifth passage. In addition leukemic spleen from another SJL/J strain mouse with spontaneous reticulum cell neoplasm (type A) was set up in tissue culture and is now in its 141st serial passage in vitro. Preliminary results indicate that cell-free material of 39th tissue culture passage can reproduce neoplasia in BALB/c mice.

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Cryo-electron microscopy of two-dimensional crystals of reduced type B botulinum neurotoxin

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100123052 ◽

1992 ◽

Vol 50 (1) ◽

pp. 530-531

Author(s):

P. F. Flicker ◽

V.S. Kulkarni ◽

J. P. Robinson ◽

G. Stubbs ◽

B. R. DasGupta

Keyword(s):

Disulfide Bonds ◽

Clostridium Botulinum ◽

Structural Changes ◽

Two Dimensional ◽

Type B ◽

Single Chain ◽

Muscle Paralysis ◽

Cryo Electron Microscopy ◽

Disulfide Linkages ◽

Intracellular Action

Botulinum toxin is a potent neurotoxin produced by Clostridium botulinum. The toxin inhibits release of neurotransmitter, causing muscle paralysis. There are several serotypes, A to G, all of molecular weight about 150,000. The protein exists as a single chain or or as two chains, with two disulfide linkages. In a recent investigation on intracellular action of neurotoxins it was reported that type B neurotoxin can inhibit the release of Ca++-activated [3H] norepinephrine only if the disulfide bonds are reduced. In order to investigate possible structural changes in the toxin upon reduction of the disulfide bonds, we have prepared two-dimensional crystals of reduced type B neurotoxin. These two-dimensional crystals will be compared with those of the native (unreduced) type B toxin.

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