Vertex operators, symmetric functions, and the spin group Γn
Vertex operators, symmetric functions, and the spin group Γn
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DOI：
10.1016/0021-8693(91)90177-a
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发表时间：
1991-04
影响因子：
0.9
通讯作者：
N. Jing
中科院分区：
文献类型：
--
作者：
N. Jing
This work provides a vertex operator approach to the symmetric group S n and its double covering group Γ n. By generalizing a result of Frenkel and Sato for S n we formulate a correspondence between the space V̂ of certain twisted vertex operators, the ring Λ of symmetric functions over Q (√ 2), and the space of nontrivial irreducible characters of Γ n. Under this identification we show that a distinguished orthogonal basis of V̂ corresponds to the set of nontrivial irreducible characters of Γ n, where both are parametrized by partitions with odd integer parts. The counterpart of this distinguished basis in the ring Λ over Q (√ 2) is the set of Schur's Q-functions, which are, loosely speaking, the square roots of the Schur functions. The nontrivial part of the character table of Γ n is shown to be given by certain matrix coefficients in V̂.
