Pfaffians and Representations of the Symmetric Group

Alain Lascoux (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

Pfaffians of matrices with entries z[i,j]/(x_i+x_j), or determinants of matrices with entries z[i,j]/(x_i-x_j), where the antisymmetrical indeterminates z[i,j] satisfy the Plücker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young's orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, and recover in particular the evaluation of Pfaffians which appeared in the recent literature.

Mots clés: Pfaffians; Symmetric Group; Representations

Domaines: Combinatoire [math.CO]

Alain Lascoux. Pfaffians and Representations of the Symmetric Group. 2006. ⟨hal-00107042⟩