Irreducible decomposition of tensor product of irreducible \$S_n\$ representations - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T22:24:33Z http://mathoverflow.net/feeds/question/64881 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/64881/irreducible-decomposition-of-tensor-product-of-irreducible-s-n-representations Irreducible decomposition of tensor product of irreducible \$S_n\$ representations George 2011-05-13T08:51:44Z 2011-05-13T20:11:56Z <p>Are there well known results on the irreducibles in the decomposition of tensor products of irreducible \$S_n\$ representations? I would also like to know of some references where I can find formulas (if they exist in the literature) for finding multiplicities. </p> http://mathoverflow.net/questions/64881/irreducible-decomposition-of-tensor-product-of-irreducible-s-n-representations/64928#64928 Answer by Richard Borcherds for Irreducible decomposition of tensor product of irreducible \$S_n\$ representations Richard Borcherds 2011-05-13T20:11:56Z 2011-05-13T20:11:56Z <p>The numbers you want are called Kronecker coefficients. Bürgisser and Ikenmeyer "<a href="http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/viewFile/dmAJ0131/2487" rel="nofollow">The complexity of computing Kronecker coefficients</a>" showed that they are hard to compute in general, so in particular there are no "easy" formulas for them. (There are some explicit formulas for simple special cases.) </p>