Zobrazeno 1 - 10
of 187
pro vyhledávání: '"Perelomov, A. M."'
We study weight multiplicities in tensor powers of the adjoint representation of $SU(3)$ and relate them to Franel numbers.
Externí odkaz:
http://arxiv.org/abs/1911.04346
Autor:
Perelomov, A. M.
By using of Euler's difference table, we obtain simple explicit formula for the decomposition of $k$-th tensor power of adjoint representation of $A_n$ Lie algebra at $2 k \le{n+1}$.
Comment: 4 pages
Comment: 4 pages
Externí odkaz:
http://arxiv.org/abs/1903.11384
Autor:
Perelomov, A. M.
In this note the simple procedure for obtaining the mass spectrum of two-dimensional Toda lattice of $E_8$ type is given.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/1903.02381
Autor:
Perelomov, A. M.
We consider the relation between Euler's trinomial problem and the problem of decomposition of tensor powers of adjoint representation of $A_1$ Lie algebra. By using this approach, some new results for both problems are obtained.
Comment: 5 page
Comment: 5 page
Externí odkaz:
http://arxiv.org/abs/1902.08065
A method based on the quantum Calogero-Sutherland model is used to obtain generating functions for characters and multiplicities of $A_3$. Some comments on other rank three algebras are offered.
Comment: 13 pages, no figures
Comment: 13 pages, no figures
Externí odkaz:
http://arxiv.org/abs/1705.03711
A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from $H$ explicit
Externí odkaz:
http://arxiv.org/abs/1506.07815
On the generating function of weight multiplicities for the representations of the Lie algebra $C_2$
We use the generating function of the characters of $C_2$ to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple Lie algebra. From this generating function we derive some recur
Externí odkaz:
http://arxiv.org/abs/1405.2758
Publikováno v:
J. Phys. A: Math. Theor. 47 (2014) 145202
We describe a general approach to obtain the generating functions of the characters of simple Lie algebras which is based on the theory of the quantum trigonometric Calogero-Sutherland model. We show how the method works in practice by means of a few
Externí odkaz:
http://arxiv.org/abs/1304.7203
Autor:
Perelomov, A. M.1 (AUTHOR) aperelomo@gmail.com
Publikováno v:
Theoretical & Mathematical Physics. Dec2022, Vol. 213 Issue 3, p1665-1668. 4p.
We provide a list of explicit eigenfunctions of the trigonometric Calogero-Sutherland Hamiltonian associated to the root system of the exceptional Lie algebra E8. The quantum numbers of these solutions correspond to the first and second order weights
Externí odkaz:
http://arxiv.org/abs/0906.2300