Proof of a conjecture of Klopsch-Voll on Weyl groups of type $A$

We give a geometric realization of the symmetric algebra of the tensor space [Formula: see text] together with the action of the dual pair (gln, glm) in terms of lagrangian cycles in the cotangent bundles of certain varieties. We establish geometrically the equivalence between the (gln, glm)-duality and Schur duality. We establish the connection between Springer's construction of (representations of) Weyl groups and Ginzburg's construction of (representations of) Lie algebras of type A.

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Weyl groups and vertex operator algebras generated by Ising vectors satisfying the (2B, 3C) condition

Reviews in Mathematical Physics ◽

10.1142/s0129055x14500111 ◽

2014 ◽

Vol 26 (06) ◽

pp. 1450011

Author(s):

Hsian-Yang Chen ◽

Ching Hung Lam

Keyword(s):

Weyl Group ◽

Root System ◽

Vertex Operator ◽

Operator Algebras ◽

Central Charge ◽

Type A ◽

Weyl Groups ◽

Vertex Operator Algebras

In this paper, we construct explicitly certain moonshine type vertex operator algebras generated by a set of Ising vectors I such that (1) for any e ≠ f ∈ I, the subVOA VOA (e, f) generated by e and f is isomorphic to either U2B or U3C; and (2) the subgroup generated by the corresponding Miyamoto involutions {τe | e ∈ I} is isomorphic to the Weyl group of a root system of type An, Dn, E6, E7 or E8. The structures of the corresponding vertex operator algebras and their Griess algebras are also studied. In particular, the central charge of these vertex operator algebras are determined.

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A Length Function for Weyl Groups of Extended Affine Root Systems of Type A1

Algebra Colloquium ◽

10.1142/s100538671500053x ◽

2015 ◽

Vol 22 (04) ◽

pp. 621-638 ◽

Cited By ~ 1

Author(s):

Saeid Azam ◽

Mohammad Nikouei

Keyword(s):

Weyl Group ◽

Root Systems ◽

Type A ◽

Length Function ◽

Weyl Groups ◽

Combinatorial Properties ◽

Affine Root Systems

In this work, we study the concept of the length function and some of its combinatorial properties for the class of extended affine root systems of type A1. We introduce a notion of root basis for these root systems, and using a unique expression of the elements of the Weyl group with respect to a set of generators for the Weyl group, we calculate the length function with respect to a very specific root basis.

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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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Hepatitis A Antigen in Liver, Bile and Stool

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100115328 ◽

1975 ◽

Vol 33 ◽

pp. 340-341

Author(s):

D.R. Jackson ◽

J.H. Hoofnagle ◽

A.N. Schulman ◽

J.L. Dienstag ◽

R.H. Purcell ◽

...

Keyword(s):

Hepatitis A ◽

Liver Enzymes ◽

Hepatitis A Virus ◽

Type A ◽

Initial Study ◽

Virus Like Particle ◽

Elevated Liver Enzymes ◽

Ag Particles ◽

Ag Particle ◽

Human Stool

Using immune electron microscopy Feinstone et. al. demonstrated the presence of a 27 nm virus-like particle in acute-phase stools of patients with viral hepatitis, type A, These hepatitis A antigen (HA Ag) particles were aggregated by convalescent serum from patients with type A hepatitis but not by pre-infection serum. Subsequently Dienstag et. al. and Maynard et. al. produced acute hepatitis in chimpanzees by inoculation with human stool containing HA Ag. During the early acute disease, virus like particles antigenically, morphologically and biophysically identical to the human HA Ag particle were found in chimpanzee stool. Recently Hilleman et. al. have described similar particles in liver and serum of marmosets infected with hepatitis A virus (HAV). We have investigated liver, bile and stool from chimpanzees and marmosets experimentally infected with HAV. In an initial study, a chimpanzee (no.785) inoculated with HA Ag-containing stool developed elevated liver enzymes 21 days after exposure.

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Detection of Viral Antigens in Mouse and Rat Tumor Cells by Immunoelectron Microscopy Following Periodate-Lysine-Paraformaldehyde (PLP) Fixation

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010009124x ◽

1976 ◽

Vol 34 ◽

pp. 252-253

Author(s):

Y. Ohtsuki ◽

G. Seman ◽

J. M. Bowen ◽

M. Scanlon ◽

L. Dmochowski

Keyword(s):

Immunoelectron Microscopy ◽

Mammary Tumor ◽

Type A ◽

Rabbit Serum ◽

Virus Particles ◽

Viral Antigens ◽

Culture Cells ◽

Mouse Mammary Tumor ◽

Tumor Virus ◽

Immunoperoxidase Labeling

Recently, periodate-lysine-paraformaldehyde (PLP) fixation was reported for immunoelectron microscopy (1). In PLP fixation, carbohydrates are oxidized by periodate and cross-linked by lysine; paraformaldehyde stabilizes proteins and lipids. By using PLP fixation, intracytoplasmic type A viral antigens have been previously demonstrated by immunoperoxidase labeling (2). In the present study, PLP fixation has been applied for the detection of the same antigens in mouse mammary tumor culture cells by both immunoferritin and immunoperoxidase methods. Rabbit anti-intracytoplasmic type A virus serum (anti-A), kindly provided by Dr. M. Muller (3), rabbit anti-strain A mouse mammary tumor virus (anti-MMTV) and preimmune rabbit serum as control were used to detect viral antigens in cells of C3H/HeJ strain mouse mammary tumor culture. Attempts have been also made to demonstrate peroxidase labeling of type C virus particles in frozen sections of an SD-MSV-induced NZB rat bone tumor tissue by rabbit anti-MuLV serum.

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