Representation theory of 0-Hecke-Clifford algebras
Representation theory of 0-Hecke-Clifford algebras
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0-Hecke-Clifford代数的表示论
DOI：
10.1016/j.jalgebra.2016.01.013
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发表时间：
2016
影响因子：
0.9
通讯作者：
Li Yunnan
中科院分区：
文献类型：
--
作者：
Li Yunnan
0-Hecke-Clifford代数作为退化代数的表示理论不是半单的，也具有丰富的组合意义。Bergeron，Hivert和Thibon证明了0-Hecke-Clifford代数的生成超模范畴的Grothendieck环同构于Stembridge定义的峰值拟对称函数代数。本文进一步研究了非生成投射超模范畴，阐明了它与对称群的峰代数之间的对应关系。特别地，得到了诱导投射超模的两类限制规则。然后，考虑相应的Heisenberg二重化及其Fock表示，证明了峰值拟对称函数环在Schur Q-函数所张成的对称函数子环上是自由的.
The representation theory of 0-Hecke–Clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning. Bergeron, Hivert and Thibon have proved that the Grothendieck ring of the category of finitely generated supermodules of 0-Hecke–Clifford algebras is isomorphic to the algebra of peak quasisymmetric functions defined by Stembridge. In this paper we further study the category of finitely generated projective supermodules and clarify the correspondence between it and the peak algebra of symmetric groups. In particular, two kinds of restriction rules for induced projective supermodules are obtained. After that, we consider the corresponding Heisenberg double and its Fock representation to prove that the ring of peak quasisymmetric functions is free over its subring of symmetric functions spanned by Schur's Q-functions.