arXiv subjects

Nhok Tkhai Shon Ngo

Publications and source records attributed to Nhok Tkhai Shon Ngo.

3 recordsLinked to original sources

arXiv2026

Indecomposable characters of the wreath product of a torus by the infinite block-diagonal symmetric group

In this paper we obtain a complete description of all indecomposable characters (central positive-definite functions) of "block-diagonal" inductive limits of semidirect products $\mathbb{T}^N\rtimes\mathfrak{S}_{N}$ of the compact $N$-dimensional torus $\mathbb{T}^{N}$ with the symmetric group $\mathfrak{S}_{N}$. The classification is proved by means of a variant of the ergodic method of Vershik and Kerov, namely by studying the weak limits of characters of finite-dimensional subgroups. As an application of our results, we give another proof of the classification of indecomposable characters of the infinite unitary group with block diagonal embeddings.

math.RT↗

arXiv2026

Big Algebra in Type $A$ for the Coordinate Ring of the Matrix Space

In this paper, we consider the big algebra recently introduced by Hausel for the $\mathrm{GL}_n$-action on the coordinate ring of the matrix space $\mathrm{Mat}(n,r)$. In particular, we obtain explicit formulas for the big algebra generators in terms of differential operators with polynomial coefficients. We show that big algebras in type $A$ are commutative and relate them to the Bethe subalgebra in the Yangian $\operatorname{Y}(\mathfrak{gl}_{n})$. We apply these results to big algebras of symmetric powers of the standard representation of $\mathrm{GL}_n$.

math.RT↗

arXiv2021

$\mathrm{GL}_n$-structure and principal $\mathfrak{sl}_2$-triple on the cohomology ring of complex Grassmannian

In this note we describe the cohomology ring of the Grassmannian of $k$-planes in $n$-dimensional complex vector space as an $\mathrm{GL}_n$-module. We give explicit formulas for the operators of its principal $\mathfrak{sl}_2$-triple. It is proved that one of these operators corresponds to the shifted cohomology degree operator and the second operator coincides with the Lefschetz map on cohomology (as in the hard Lefschetz theorem). We check that the cohomology ring of the complex Grassmannian as a $\mathrm{GL}_n$-representation is isomorphic to the $k$-th exterior power of the standard $n$-dimensional representation.

math.AG↗