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 $({\rm SL}_{2n+1}({\rm C}), {\rm Sp}_{2n}({\rm C}))$.

中文翻译：

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特殊线性群与经典群上张量积的多重性

在本文中，使用通过 LiE 软件完成的计算，我们比较了特殊线性群的不可约自对偶表示的张量积与经典群的张量积，以制定有关两者的一些猜想。在这个过程中，出现了一些其他现象，我们将它们记录为问题。更准确地说，在 ${\rm SL}_{2n}({\mathbb C})$ 与 ${\rm Spin}_{2n+1}({\ mathbb C})$，很容易看出，如果 ${\rm Spin}_{2n+1}({\rm C})$ 的三个不可约表示的张量积包含平凡表示，那么${\rm SL}_{2n}({\rm C})$ 的相应表示的张量积。论文提出了一个相反方向的猜想。