scholarly journals Promotion Operator on Rigged Configurations of Type $A$

10.37236/296 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Anne Schilling ◽  
Qiang Wang
Keyword(s):  
Tensor Products ◽  
Type A ◽  
Rigged Configurations ◽  
Promotion Operator

In an earlier paper of the first author, the analogue of the promotion operator on crystals of type $A$ under a generalization of the bijection of Kerov, Kirillov and Reshetikhin between crystals (or Littlewood–Richardson tableaux) and rigged configurations was proposed. In this paper, we give a proof of this conjecture. This shows in particular that the bijection between tensor products of type $A_n^{(1)}$ crystals and (unrestricted) rigged configurations is an affine crystal isomorphism.

scholarly journals A promotion operator on rigged configurations

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Qiang Wang
Keyword(s):  
Type A ◽  
Rigged Configurations ◽  
International Audience ◽  
Promotion Operator

International audience In a recent paper, Schilling proposed an operator $\overline{\mathrm{pr}}$ on unrestricted rigged configurations $RC$, and conjectured it to be the promotion operator of the type $A$ crystal formed by $RC$. In this paper we announce a proof for this conjecture.

scholarly journals Tensor products and restrictions in type A

2012 ◽  
Author(s):  
Jonathan Brundan ◽  
Alexander S. Kleshchev
Keyword(s):  
Tensor Products ◽  
Type A

scholarly journals THE COMBINATORICS OF TENSOR PRODUCTS OF HIGHER AUSLANDER ALGEBRAS OF TYPE A

2020 ◽  
pp. 1-21
Author(s):  
JORDAN MCMAHON ◽  
NICHOLAS J. WILLIAMS
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Type A ◽  
Coordinate Ring ◽  
Preprojective Algebra ◽  
Finite Algebras ◽  
Plücker Coordinates ◽  
Higher Dimensional ◽  
Dimensional Version

Abstract We consider maximal non-l-intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Plücker coordinates in the Grassmannian coordinate ring, as described by Scott. We extend a method of Scott for producing such collections, which are related to tensor products of higher Auslander algebras of type A. We show that a higher preprojective algebra of the tensor product of two d-representation-finite algebras has a d-precluster-tilting subcategory. Finally, we relate mutations of these collections to a form of tilting for these algebras.

scholarly journals On the uniqueness of promotion operators on tensor products of type A crystals

2009 ◽  
Vol 31 (2) ◽  
pp. 217-251 ◽  
Author(s):  
Jason Bandlow ◽  
Anne Schilling ◽  
Nicolas M. Thiéry
Keyword(s):  
Tensor Products ◽  
Type A

scholarly journals Crystal Structure on Rigged Configurations and the Filling Map

10.37236/4674 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Anne Schilling ◽  
Travis Scrimshaw
Keyword(s):  
Crystal Structure ◽  
Tensor Products ◽  
Tensor Factor ◽  
Rigged Configurations

In this paper, we extend work of the first author on a crystal structure on rigged configurations of simply-laced type to all non-exceptional affine types using the technology of virtual rigged configurations and crystals. Under the bijection between rigged configurations and tensor products of Kirillov--Reshetikhin crystals specialized to a single tensor factor, we obtain a new tableaux model for Kirillov--Reshetikhin crystals. This is related to the model in terms of Kashiwara--Nakashima tableaux via a filling map, generalizing the recently discovered filling map in type $D_n^{(1)}$.

scholarly journals On tensor products of path algebras of type A

2014 ◽  
Vol 448 ◽  
pp. 222-244
Author(s):  
Lutz Hille ◽  
Jürgen Müller
Keyword(s):  
Tensor Products ◽  
Type A ◽  
Path Algebras

scholarly journals Stable rigged configurations and Littlewood―Richardson tableaux

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Masato Okado ◽  
Reiho Sakamoto
Keyword(s):  
Dynkin Diagram ◽  
Type A ◽  
Affine Algebra ◽  
Large Rank ◽  
Rigged Configurations ◽  
International Audience

International audience For an affine algebra of nonexceptional type in the large rank we show the fermionic formula depends only on the attachment of the node 0 of the Dynkin diagram to the rest, and the fermionic formula of not type $A$ can be expressed as a sum of that of type $A$ with Littlewood–Richardson coefficients. Combining this result with theorems of Kirillov–Schilling–Shimozono and Lecouvey–Okado–Shimozono, we settle the $X=M$ conjecture under the large rank hypothesis. Pour une algèbre affine de type non-exceptionnel de grand rang nous prouvons que la formule fermionique dépend seulement du voisinage du nœud 0 dans le diagramme de Dynkin, et également que la formule fermionique en type autre que $A$ peut être exprimée comme combinaison de celles de type $A$ avec des coefficients de Littlewood–Richardson. Combinant ce résultat avec des théorèmes de Kirillov–Schilling–Shimozono et de Lecouvey–Okado–Shimozono, nous résolvons la conjecture $X=M$ lorsque le rang est grand.

scholarly journals ON TENSOR PRODUCTS OF A MINIMAL AFFINIZATION WITH AN EXTREME KIRILLOV-RESHETIKHIN MODULE FOR TYPE A

2017 ◽  
Vol 23 (4) ◽  
pp. 989-1044 ◽  
Author(s):  
A. MOURA ◽  
F. PEREIRA
Keyword(s):  
Tensor Products ◽  
Type A

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

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.

Hepatitis A Antigen in Liver, Bile and Stool

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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