Generating functions for permutation representations

We discuss the categorical approach to representations in wreath products, and generalize the Wohlfahrt formula of the exponential generating function for the number of permutation representations

The number of subgroups of a finite group (II)

Let A be a finite group, and let p be a prime. Suppose that ps is the highest power of p dividing |A/A\u27|, where A\u27 is the commutator subgroup of A, and that the type λ=(λ1, λ2,…) with λ1≥λ2≥⋯ of a Sylow p-subgroup of A/A\u27 satisfies either λ2≤1 or λ2=2 and λ3=0. Let mA(d) denote the number of subgroups of index d in A. If 1≤i≤[(s+1)/2] and q is a positive integer such that gcd(p,q)=1, then mA(qpi−1)−mA(qpi) is a multiple of pi and mA(qp[(s+1)/2])−mA(qp[(s+1)/2]+1) is a multiple of p[s/2]

Microscopic Aspects of Multipole Properties of Filled Skutterudites

We discuss low-temperature multipole states of Nd-based filled skutterudites by analyzing a multiorbital Anderson model with the use of a numerical renormalization group method. In order to determine the multipole state, we take a procedure to maximize the multipole susceptibility matrix. Then, it is found that the dominant multipole state is characterized by the mixture of 4u magnetic and 5u octupole moments. The secondary state is specified by 2u octupole. When we further take into account the coupling between $f$ electrons in degenerate $\Gamma_{67}^{-}$ ($e_{\rm u}$) orbitals and dynamical Jahn-Teller phonons with $E_{\rm g}$ symmetry, quadrupole fluctuations become significant at low temperatures in the mixed multipole state with 4u magnetic and 5u octupole moments. Finally, we briefly discuss possible relevance of the present results to actual Nd-based filled skutterudite compounds.Comment: 6 pages, 3 figures. To appear in the Proceedings of the 17th International Conference on Magnetism (ICM2006

The units of a partial Burnside ring relative to the Young subgroups of a symmetric group

The unit group of a partial Burnside ring relative to the Young subgroups of the symmetric group SnSn on n letters is included in the image by the tom Dieck homomorphism. As a consequence of this fact, the alternating character νnνn of SnSn is expressed explicitly as a ZZ-linear combinations of permutation characters associated with finite left SnSn-sets Sn/YSn/Y for the Young subgroups Y.Mathematics Subject Classification. Primary 19A22, Secondary 20B35; 20C15; 20C3

Optical conductivity of filled skutterudites

A simple tight-binding model is constructed for the description of the electronic structure of some Ce-based filled skutterudite compounds showing an energy gap or pseudogap behavior. Assuming band-diagonal electron interactions on this tight-binding model, the optical conductivity spectrum is calculated by applying the second-order self-consistent perturbation theory to treat the electron correlation. The correlation effect is found to be of great importance on the description of the temperature dependence of the optical conductivity. The rapid disappearance of an optical gap with increasing temperature is obtained as observed in the optical experiment for Ce-based filled-skutterudite compounds.Comment: 6 pages, 7 figures, use jpsj2.cls, to appear in J. Phys. Soc. Jpn. Vol.73, No.10 (2004