论文标题
外部代数的准对称谐波
Quasisymmetric harmonics of the exterior algebra
论文作者
论文摘要
我们研究了$ n $ antymuting（费米子）变量中的准对称多项式环。令$ r_n $表示$ n $抗议变量中的多项式。本文的主要结果表明了以下有关抗压变量中的准对称多项式的有趣事实： （1）$ r_n $中的准对象多项式形式形成$ r_n $的交换子代数。 （2）由$ r_n $中的$ r_n $生成的理想$ i_n $的$ r_n $的商的基础是通过投票序列索引的。希尔伯特一系列商系列由 $ \ text {hilb} _ {r_n/i_n}（q）= \ sum_ {k = 0}^{\ lfloor {\ lfloor {n/2} \ rfloor} f^{（n-k，k，k，k）} $（n-k，k）$。 （3）有一个由准对称多项式产生的理想的基础，该理想是由打破投票条件的序列索引的
We study the ring of quasisymmetric polynomials in $n$ anticommuting (fermionic) variables. Let $R_n$ denote the polynomials in $n$ anticommuting variables. The main results of this paper show the following interesting facts about quasisymmetric polynomials in anticommuting variables: (1) The quasisymmetric polynomials in $R_n$ form a commutative sub-algebra of $R_n$. (2) There is a basis of the quotient of $R_n$ by the ideal $I_n$ generated by the quasisymmetric polynomials in $R_n$ that is indexed by ballot sequences. The Hilbert series of the quotient is given by $$ \text{Hilb}_{R_n/I_n}(q) = \sum_{k=0}^{\lfloor{n/2}\rfloor} f^{(n-k,k)} q^k\,,$$ where $f^{(n-k,k)}$ is the number of standard tableaux of shape $(n-k,k)$. (3) There is a basis of the ideal generated by quasisymmetric polynomials that is indexed by sequences that break the ballot condition
