论文标题
特殊线性与经典组的张量产品的繁殖力
Multiplicities for tensor products on Special linear versus Classical groups
论文作者
论文摘要
在本文中，使用通过Lie软件进行的计算，我们比较了特殊线性组的不可还原自我表示的张量产品与经典组的张量产品，以提出与两者有关的一些猜想。在此过程中，我们将自己记录为问题的其他一些现象。 更准确地说，在$ {\ rm sl} _ {2n}（{\ Mathbb c}）$ $ {\ rm sl} _ {\ rm spin} _ {\ rm spin} _ {\ rm spin} _ {2n+1}（{\ mathbb c}）的自然对应下$ {\ rm spin} _ {2n+1}（{\ rm c}）$包含琐碎的表示，那么$ {\ rm sl} _ {2n}的相应表示的张量产品也是如此。本文在反向方向上提出了猜想。我们还处理$（{\ rm sl} _ {2n+1}（{\ rm c}），{\ rm sp} _ {2n}（{\ rm c}））$。
In this paper, using computations done through the LiE software, we compare the tensor product of irreducible selfdual representations of the special linear group with those of classical groups to formulate some conjectures relating the two. In the process a few other phenomenon present themselves which we record as questions. More precisely, under the natural correspondence of irreducible finite dimensional selfdual representations of ${\rm SL}_{2n}({\mathbb C})$ with those of ${\rm Spin}_{2n+1}({\mathbb C})$, it is easy to see that if the tensor product of three irreducible representations of ${\rm Spin}_{2n+1}({\rm C})$ contains the trivial representation, then so does the tensor product of the corresponding representations of ${\rm SL}_{2n}({\rm C})$. The paper formulates a conjecture in the reverse direction. We also deal with the pair $({\rm SL}_{2n+1}({\rm C}), {\rm Sp}_{2n}({\rm C}))$.
