论文标题
组合类型的组合双重性
Combinatorial Howe duality of symplectic type
论文作者
论文摘要
我们给出了形式的双对$（\ g，{\ rm sp} _ {2 \ ell}）$的新组合解释，其中$ \ g $是经典类型的谎言（超级）代数。这是通过建立与该对相关的RSK算法的符号类似物来完成的，该算法均不取决于$ \ g $。我们介绍了Jeu de Taquin滑动的类似物，以供谎言superalgebra $ \ g $的旋转模型定义$ p $ -tableau，并表明相关的$ q $ -Tableau由国王造成的Symplectic tableau给出。
We give a new combinatorial interpretation of Howe dual pairs of the form $(\g,{\rm Sp}_{2\ell})$, where $\g$ is a Lie (super)algebra of classical type. This is done by establishing a symplectic analogue of the RSK algorithm associated to this pair, in a uniform way which does not depend on $\g$. We introduce an analogue of jeu de taquin sliding for spinor model of irreducible characters of a Lie superalgebra $\g$ to define $P$-tableau and show that the associated $Q$-tableau is given by a symplectic tableau due to King.
