Skew Young diagram method in spectral decomposition of integrable lattice models

Details Skew Young diagram method in spectral decomposition of integrable lattice models Skew Young diagram method in spectral decomposition of integrable lattice models

1996-07-19

arxiv.org/abs/q-alg/9607027v1

Commun.Math.Phys. 185 (1997) 441-465

Physics

High Energy Physics

High Energy Physics - Theory

AMS-LaTeX, 28 pages

Scientific paper

10.1007/s002200050098

The spectral decomposition of the path space of the vertex model associated to the vector representation of the quantized affine algebra $U_q(\hat{sl}_n)$ is studied. We give a one-to-one correspondence between the spin configurations and the semi-standard tableaux of skew Young diagrams. As a result we obtain a formula of the characters for the degeneracy of the spectrum in terms of skew Schur functions. We conjecture that our result describes the $sl_n$-module contents of the Yangian $Y(sl_n)$-module structures of the level 1 integrable modules of the affine Lie algebra $\hat{sl}_n$. An analogous result is obtained also for a vertex model associated to the quantized twisted affine algebra $U_q(A^{(2)}_{2n})$, where $Y(B_n)$ characters appear for the degeneracy of the spectrum. The relation to the spectrum of the Haldane-Shastry and the Polychronakos models are also discussed.

Affiliated with

Also associated with

No associations

Rating

Skew Young diagram method in spectral decomposition of integrable lattice models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Skew Young diagram method in spectral decomposition of integrable lattice models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Skew Young diagram method in spectral decomposition of integrable lattice models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-620617