相关论文: Demazure crystals of generalized Verma modules and…
We give an affine analogue of the Robison-Schensted-Knuth (RSK) correspondence, which generalizes the affine Robinson-Schensted correspondence by Chmutov-Pylyavskyy-Yudovina. The affine RSK map sends a generalized affine permutation of…
The Robinson-Schensted-Knuth (RSK) correspondence is a bijective correspondence between two-rowed arrays of non-negative integers and pairs of same-shape semistandard tableaux. This correspondence satisfies the symmetry property, that is,…
We present a Robinson-Schensted-Knuth type one-to-one correspondence between the set of pictures and the set of pairs of Littlewood-Richardson crystals.
The set of orbits of $GL(V)$ in $Fl(V)\times Fl(V)\times V$ is finite, and is parametrized by the set of certain decorated permutations in a work of Solomon. We describe a Mirabolic RSK correspondence (bijective) between this set of…
The classical Robinson--Schensted--Knuth correspondence is a bijection from nonnegative integer matrices to pairs of semi-standard Young tableaux. Based on the work of, among others, Burge, Hillman, Grassl, Knuth and Gansner, it is known…
The RSK correspondence generalises the Robinson-Schensted correspondence by replacing permutation matrices by matrices with entries in ${\bf N}$, and standard Young tableaux by semistandard ones. For $r>0$, the Robinson-Schensted…
We study asymptotic properties of sequences of partitions ($\sigma$\nobreakdash-algebras) in spaces with Bernoulli measures associated with the Robinson--Schensted--Knuth correspondence.
We continue work begun in \cite{ptab} which introduced \emph{perforated tableaux} as a combinatorial model for crystals of type $A_{n-1}$, emphasizing connections to the classical Robinson-Schensted-Knuth (RSK) correspondence and Lusztig…
We give a combinatorial realization of a level-$\ell$ Robinson-Schensted-Knuth correspondence conjectured to exist by Song and Wang for cyclotomic Schur categories. We show that cyclotomic basis elements can be canonically reorganized into…
Let $\lambda=(\lambda_1 \geqslant \ldots \geqslant \lambda_k > 0)$. For any $c$ Coxeter element of $\mathfrak{S}_{\lambda_1+k-1}$, we construct a bijection from fillings of $\lambda$ to reverse plane partitions. We recover two previous…
Although the Robinson-Schensted-Knuth correspondence is a classical subject, its study is still active because of new development in last two decades. In this field, fundamental results are sometimes proved by using machineries which may be…
The crystal base of the modified quantized enveloping algebras of type $A_{+\infty}$ or $A_\infty$ is realized as a set of integral bimatrices. It is obtained by describing the decomposition of the tensor product of a highest weight crystal…
We are interested in the structure of the crystal graph of level $l$ Fock spaces representations of $\mathcal{U}_q (\widehat{\mathfrak{sl}_e})$. Since the work of Shan [26], we know that this graph encodes the modular branching rule for a…
R. Sulzgruber's rim hook insertion and the Hillman-Grassl correspondence are two distinct bijections between the reverse plane partitions of a fixed partition shape and multisets of rim-hooks of the same partition shape. It is known that…
In this paper, we study a tensor product of perfect Kirillov-Reshetikhin crystals (KR crystals for short) whose levels are not necessarily equal. We show that, by tensoring with a certain highest weight element, such a crystal becomes…
We construct new "standard modules" for the representations of general linear groups over a local non-archimedean field. The construction uses a modified Robinson-Schensted-Knuth correspondence for Zelevinsky's multisegments. Typically, the…
The tensor powers of the vector representation associated to an infinite rank quantum group decompose into irreducible components with multiplicities independant of the infinite root system considered. Although the irreducible modules…
We introduce the dual affine Robinson-Schensted correspondence that gives a bijection between the extended affine symmetric group and tuples $(\bar{P},\bar{Q},\lambda,N)$, where $\bar{P}$ and $\bar{Q}$ are tabloids, $\lambda$ is a…
Motivated by classical combinatorial Schubert calculus on the Grassmannian, Huang--Pylyavskyy introduced a generalized theory of Robinson-Schensted-Knuth (RSK) correspondence for studying Schubert calculus on the complete flag variety via…
We show that a tensor product of nonexceptional type Kirillov--Reshetikhin (KR) crystals is isomorphic to a direct sum of Demazure crystals; we do this in the mixed level case and without the perfectness assumption, thus generalizing a…