Polytopes associated to dihedral groups

Polynomials Associated with Dihedral Groups

Abstract. There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial derivatives. This paper presents an explicit form of the action of the intertwining operator on polynomials by use of harmonic and Jacobi polynomials. The ...

Vector Polynomials and a Matrix Weight Associated to Dihedral Groups

The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case for even dihedral groups). The matrix weight function for the Gaussian form is found explicitly by solving a boundary value problem, and then computing the n...

Dihedral Groups

fixed point property for banach algebras associated to locally compact groups

در این پایان نامه به بررسی خاصیت نقطه ثابت و خاصیت نقطه ثابت برای نیم گروههای برگشت پذیر چپ روی بعضی جبرهای باناخ از جمله جبر فوریه و جبر فوریه استیلتیس پرداخته شده است. برای مثال بیان شده است که اگر گروه یک گروه فشرده موضعی با همسایگی فشرده برای عنصر همانی که تحت درونریختی ها پایاست باشد آنگاه جبر فوریه و جبر فوریه استیلتیس دارای خاصیت نقطه ثابت برای نیم گروه های برگشت پذیر چپ است اگر و تنها ا...

Sumsets in dihedral groups

Let Dn be the dihedral group of order 2n. For all integers r, s such that 1 ≤ r, s ≤ 2n, we give an explicit upper bound for the minimal size μDn (r, s) = min |A · B| of sumsets (product sets) A · B, where A and B range over all subsets of Dn of cardinality r and s respectively. It is shown by construction that μDn (r, s) is bounded above by the known value of μG (r, s), where G is any abelian ...