Let C be a cyclic subgroup of S\_n.
How does the representation $Ind\_C^{S\_n}\rho$, where $\rho$ is some representation of $C$, decompose into irreducible components? 
Is there are a way to know which components appear with multiplicity 1?



Decomposition of induced representations in S_n
There is a combinatorial way to decompose $Res\_C^{S\_n}S^\lambda$ for an irreducible $S\_n$-module $S^\lambda$. We use the notion of the "major index" for a standard tabuleau of shape $\lambda$. If $C=C\_n$, the result is obtained by [Kraśkiewiz-Weyman](http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=JOUR&pg8=ET&r=1&review_format=html&s4=Weyman&s5=Coxeter&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq). See also [Garsia's paper "Combinatorics of the free Lie algebra and the symmetric group"](http://www.ams.org/mathscinet/search/publdoc.html?pg1=MR&s1=1039352&loc=fromreflist)(Theorem 8.4) and [Reutenauer's book "Free Lie algebras"](http://www.ams.org/mathscinet/search/publdoc.html?pg1=MR&s1=1231799&loc=fromreflist)(Theorem 8.8 and 8.9). This result can be generalized to any cyclic subgroup in [Jöllenbeck-Schocker's paper "Cyclic characters of symmetric groups"](http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=JOUR&pg8=ET&review_format=html&s4=&s5=cyclic%20character&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=3&mx-pid=1801229).


