Geodesic
Shapovalov elements and Hasse diagrams
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 3, pp. 405-416

Voir la notice de l'article provenant de la source Math-Net.Ru

Shapovalov elements of quantum groups are special polynomials in negative simple root vectors with coefficients in the rational Cartan subalgebra that relate singular vectors in reducible Verma modules with their highest vectors. We give explicit expressions for Shapovalov elements of nonexceptional quantum groups in terms of matrix elements of quantum $L$-operators using calculations on Hasse diagrams associated with auxiliary representations.
Keywords: Shapovalov elements, Hasse diagrams.
Mots-clés : $R$-matrix, Verma modules 
@article{TMF_2023_216_3_a2,
     author = {D. Algethami and A. I. Mudrov},
     title = {Shapovalov elements and {Hasse} diagrams},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {405--416},
     publisher = {mathdoc},
     volume = {216},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a2/}
}
TY  - JOUR
AU  - D. Algethami
AU  - A. I. Mudrov
TI  - Shapovalov elements and Hasse diagrams
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 405
EP  - 416
VL  - 216
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a2/
LA  - ru
ID  - TMF_2023_216_3_a2
ER  - 
%0 Journal Article
%A D. Algethami
%A A. I. Mudrov
%T Shapovalov elements and Hasse diagrams
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 405-416
%V 216
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a2/
%G ru
%F TMF_2023_216_3_a2
D. Algethami; A. I. Mudrov. Shapovalov elements and Hasse diagrams. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 3, pp. 405-416. http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a2/