Wave graph bases of tensor invariants of classical Lie groups and algebras

Aleksandrs Mihailovs
Department of Mathematical Sciences
SUNY College at Oneonta
Oneonta, NY 13820
Alec@Mihailovs.com
http://www.mihailovs.com/Alec/

Date: October 1, 1998

Abstract:

Introduced in author's thesis [1], wave graphs give us a new combinatorial approach to the representations and invariants of classical Lie groups and algebras. For example, wave graphs

Wave graphs

correspond to the following invariants of and :

$\displaystyle \left( (x\wedge y\wedge z)\otimes(x\wedge y\wedge z)\right)^{(34)}, \quad \left( (\omega\wedge\omega)\otimes\omega\right)^{(465)}$

where $\omega=p_1\wedge q_1 + p_2\wedge q_2$ .

Bibliography

1.: ALEKSANDRS MIHAILOVS. A Combinatorial Approach to Representations of Lie Groups and Algebras. PhD thesis, University of Pennsylvania, 1998. (dvi, ps, pdf)