scholarly journals On the semisimplicity of the cyclotomic quiver Hecke algebra of type $C$

2017 ◽  
Vol 146 (5) ◽  
pp. 1845-1857
Author(s):  
Liron Speyer
Keyword(s):  
Hecke Algebra ◽  
Type C ◽  
Quiver Hecke Algebra

scholarly journals Path combinatorics and light leaves for quiver Hecke algebras

2021 ◽  
Author(s):  
Chris Bowman ◽  
Anton Cox ◽  
Amit Hazi ◽  
Dimitris Michailidis
Keyword(s):  
Structural Information ◽  
Hecke Algebras ◽  
Symmetric Groups ◽  
Hecke Algebra ◽  
Classical Notion ◽  
Geometric Setting ◽  
Quiver Hecke Algebra

AbstractWe recast the classical notion of “standard tableaux" in an alcove-geometric setting and extend these classical ideas to all “reduced paths" in our geometry. This broader path-perspective is essential for implementing the higher categorical ideas of Elias–Williamson in the setting of quiver Hecke algebras. Our first main result is the construction of light leaves bases of quiver Hecke algebras. These bases are richer and encode more structural information than their classical counterparts, even in the case of the symmetric groups. Our second main result provides path-theoretic generators for the “Bott–Samelson truncation" of the quiver Hecke algebra.

scholarly journals A classification of SU(d)-type C*-tensor categories

2014 ◽  
Vol 25 (09) ◽  
pp. 1450081 ◽  
Author(s):  
Bas P. A. Jordans
Keyword(s):  
Tensor Category ◽  
Hecke Algebra ◽  
Sufficient Condition ◽  
Tensor Categories ◽  
Fusion Ring ◽  
Type C ◽  
Markov Trace

Kazhdan and Wenzl classified all rigid tensor categories with fusion ring isomorphic to the fusion ring of the group SU(d). In this paper we consider the C*-analogue of this problem. Given a rigid C*-tensor category 𝒞 with fusion ring isomorphic to the fusion ring of the group SU(d), we can extract a constant q from 𝒞 such that there exists a *-representation of the Hecke algebra Hn(q) into 𝒞. The categorical trace on 𝒞 induces a Markov trace on Hn(q). Using this Markov trace and a representation of Hn(q) in [Formula: see text] we show that 𝒞 is equivalent to a twist of the category [Formula: see text]. Furthermore a sufficient condition on a C*-tensor category 𝒞 is given for existence of an embedding of a twist of [Formula: see text] in 𝒞.

scholarly journals A NONSYMMETRIC VERSION OF OKOUNKOV’S BC-TYPE INTERPOLATION MACDONALD POLYNOMIALS

2021 ◽  
Author(s):  
NIELS DISVELD ◽  
TOM H. KOORNWINDER ◽  
JASPER V. STOKMAN
Keyword(s):  
Hecke Algebra ◽  
Macdonald Polynomials ◽  
Laurent Polynomials ◽  
Type Interpolation ◽  
Type C

AbstractNonsymmetric interpolation Laurent polynomials in n variables are introduced, with the interpolation points depending on q and on a n-tuple of parameters τ = (τ1, …, τn). When τi = stn − 1, Okounkov’s 3-parameter BCn-type interpolation Macdonald polynomials are recovered from the nonsymmetric interpolation Laurent polynomials through Hecke algebra symmetrisation with respect to a type Cn Hecke algebra action. In the Appendix we give some conjectures about extra vanishing, based on Mathematica computations in rank two.

Biological and Surface Properties of C-Type Virus Particles Produced by Novikoff Ascites Hepatoma Cells

1977 ◽  
Vol 35 ◽  
pp. 388-389
Author(s):  
D.C. Hixson ◽  
J.C. Chan ◽  
J.M. Bowen ◽  
E.F. Walborg
Keyword(s):  
Surface Properties ◽  
Ricinus Communis ◽  
Rat Kidney ◽  
Leukemia Virus ◽  
Viral Envelope ◽  
Virus Particles ◽  
Chemically Induced ◽  
Sarcoma Virus ◽  
Hepatocarcinoma Cells ◽  
Type C

Several years ago Karasaki (1) reported the production of type C virus particles by Novikoff ascites hepatocarcinoma cells. More recently, Weinstein (2) has reported the presence of type C virus particles in cell cultures derived from transplantable and primary hepatocellular carcinomas. To date, the biological function of these virus and their significance in chemically induced hepatocarcinogenesis are unknown. The present studies were initiated to determine a possible role for type C virus particles in chemically induced hepatocarcinogenesis. This communication describes results of studies on the biological and surface properties of type C virus associated with Novikoff hepatocarcinoma cells.Ecotropic and xenotropic murine leukemia virus (MuLV) activity in ascitic fluid of Novikoff tumor-bearing rats was assayed in murine sarcoma virus transformed S+L- mouse cells and S+L- mink cells, respectively. The presence of sarcoma virus activity was assayed in non-virus-producing normal rat kidney (NRK) cells. Ferritin conjugates of concanavalin A (Fer-Con wheat germ agglutinin (Fer-WGA), and Ricinus communis agglutinins I and II (Fer-RCAI and Fer-RCAII) were used to probe the structure and topography of saccharide determinants present on the viral envelope.

Recent Studies on a Murine Leukemia Virus Grown in Tissue Culture

1967 ◽  
Vol 25 ◽  
pp. 106-107
Author(s):  
L. Z. de Tkaczevski ◽  
E. de Harven ◽  
C. Friend
Keyword(s):  
Tissue Culture ◽  
Solid Tumors ◽  
Murine Leukemia Virus ◽  
Leukemia Virus ◽  
Supernatant Fluid ◽  
Virus Particles ◽  
Friend Leukemia ◽  
Type C ◽  
Leukemia Viruses ◽  
Murine Leukemia

Despite extensive studies, the correlation between the morphology and pathogenicity of murine leukemia viruses (MLV) has not yet been clarified. The virus particles found in the plasma of leukemic mice belong to 2 distinct groups, 1 or 2% of them being enveloped A particles and the vast majority being of type C. It is generally believed that these 2 types of particles represent different phases in the development of the same virus. Particles of type A have been thought to be an earlier form of type C particles. One of the tissue culture lines established from Friend leukemia solid tumors has provided the material for the present study. The supernatant fluid of the line designated C-1A contains an almost pure population of A particles as illustrated in Figure 1. The ratio is, therefore, the reverse of what is unvariably observed in the plasma of leukemic mice where C particles predominate.

Spontaneous Production of Type C Virus Particles in a Culture Derived from Rat Embryo Cells

1972 ◽  
Vol 30 ◽  
pp. 288-289
Author(s):  
Elizabeth S. Priori ◽  
T. Shigematsu ◽  
B. Myers ◽  
L. Dmochowski
Keyword(s):  
Virus Particle ◽  
Mouse Embryo ◽  
Calf Serum ◽  
Embryo Cell ◽  
Virus Particles ◽  
Extracellular Virus ◽  
Mouse Embryo Cell ◽  
Mature Virus Particle ◽  
Embryo Cells ◽  
Type C

Spontaneous release of type C virus particles in long-term cultures of mouse embryo cells as well as induction of similar particles in mouse embryo cell cultures with IUDR or BUDR have been reported. The presence of type C virus particles in cultures of normal rat embryos has not been reported.NB-1, a culture derived from embryos of a New Zealand Black (NB) rat (rats obtained from Mr. Samuel M. Poiley, N.C.I., Bethesda, Md.) and grown in McCoy's 5A medium supplemented with 20% fetal calf serum was passaged weekly. Extracellular virus particles similar to murine leukemia particles appeared in the 22nd subculture. General appearance of cells in passage 23 is shown in Fig. 1. Two budding figures and one immature type C virus particle may be seen in Fig. 2. The virus particles and budding were present in all further passages examined (currently passage 39). Various stages of budding are shown in Figs. 3a,b,c,d. Appearance of a mature virus particle is shown in Fig. 4.

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