Geodesic
The Jordan block structure of unipotent elements in Weyl modules for groups of type $A_1$ over a field of positive characteristic
Trudy Instituta matematiki, Tome 21 (2013) no. 2, pp. 70-72.

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

The Jordan block structure of unipotent elements in Weyl modules for an algebraic group of type $A_1$ in a positive characteristic $p$ is described. The following theorem is proved. Theorem. Let $K$ be an algebraically closed field of characteristic $p>0$ and $G=A_1(K).$ Assume that $\lambda=ip+j$ and $i,j\ge0,$ $j$ Then a nontrivial unipotent element of $G$ has $i$ Jordan blocks of size $p$ and one block of size $j+1$ in the Weyl module of $G$ with highest weight $\lambda$. Here the weights of $G$ are naturally identified with the integers. This theorem can be useful for investigating the Jordan block structure of unipotent elements in modular representations of simple algebraic groups and finite Chevalley groups. 
@article{TIMB_2013_21_2_a2,
     author = {T. S. Busel},
     title = {The {Jordan} block structure of unipotent elements in {Weyl} modules for groups of type $A_1$ over a field of positive characteristic},
     journal = {Trudy Instituta matematiki},
     pages = {70--72},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2013_21_2_a2/}
}
TY  - JOUR
AU  - T. S. Busel
TI  - The Jordan block structure of unipotent elements in Weyl modules for groups of type $A_1$ over a field of positive characteristic
JO  - Trudy Instituta matematiki
PY  - 2013
SP  - 70
EP  - 72
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2013_21_2_a2/
LA  - ru
ID  - TIMB_2013_21_2_a2
ER  - 
%0 Journal Article
%A T. S. Busel
%T The Jordan block structure of unipotent elements in Weyl modules for groups of type $A_1$ over a field of positive characteristic
%J Trudy Instituta matematiki
%D 2013
%P 70-72
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2013_21_2_a2/
%G ru
%F TIMB_2013_21_2_a2
T. S. Busel. The Jordan block structure of unipotent elements in Weyl modules for groups of type $A_1$ over a field of positive characteristic. Trudy Instituta matematiki, Tome 21 (2013) no. 2, pp. 70-72. http://geodesic.mathdoc.fr/item/TIMB_2013_21_2_a2/

[1] Proud R., Saxl J., Testerman D., “Subgroups of type $A_1$ containing a fixed unipotent element in an algebraic group”, J. Algebra, 231:1 (2000), 53–66 | DOI | MR | Zbl

[2] Suprunenko I. D., “Minimalnye polinomy elementa poryadka $p$ v neprivodimykh predstavleniyakh grupp Shevalle nad polyami kharakteristiki $p$”, Problemy algebry i logiki, Tr. In-ta matematiki SO RAN, 30, 1996, 126–163 | Zbl

[3] Steinberg R., Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR | Zbl

[4] Burbaki N., Gruppy i algebry Li, Mir, M., 1978 | MR

[5] Borel A., “Properties and linear representations of Chevalley groups”, Seminar on Algebraic Groups and Related Finite Groups 1968/69 (Berlin), Lecture Notes in Mathematics, 131, Springer, 1970, A1–A55 | MR