论文标题
模棱两可的日志coven和eproivariantkähler软件包
Equivariant log-concavity and equivariant Kähler packages
论文作者
论文摘要
我们表明，外部代数$λ_{r} \ left [α_{1}，\ cdots，α_{n} \ right] $，这是圆环$ t =（s^{1}）的同时学\ ldots，t_ {n} \ right] $，这是分类空间$ b（s^{1}）^{n} = \ left（\ Mathbb {c} \ Mathbb {c} \ Mathbb {p}^p}^{\ inftty} {\ infty} {\ right）我们这样做是通过明确给出$ s_ {n} $ - 表示多项式或外部功率张量产物的适当序列的表示图，并证明这些映射满足了硬Lefschetz定理。此外，我们证明了整个Kähler包装，包括庞加莱二元性的代数类比，硬Lefschetz和Hodge-riemann双线性关系，都在e术环境中保持相应的序列。
We show that the exterior algebra $Λ_{R}\left[α_{1}, \cdots, α_{n}\right]$, which is the cohomology of the torus $T=(S^{1})^{n}$, and the polynomial ring $\mathbb{R}\left[t_{1}, \ldots, t_{n}\right]$, which is the cohomology of the classifying space $B (S^{1})^{n}=\left(\mathbb{C} \mathbb{P}^{\infty}\right)^{n}$, are $S_{n}$-equivariantly log-concave. We do so by explicitly giving the $S_{n}$-representation maps on the appropriate sequences of tensor products of polynomials or exterior powers and proving that these maps satisfy the hard Lefschetz theorem. Furthermore, we prove that the whole Kähler package, including algebraic analogies of the Poincaré duality, hard Lefschetz, and Hodge-Riemann bilinear relations, holds on the corresponding sequences in an equivariant setting.
