Elliptic Littlewood identities

نویسنده

  • Eric M. Rains
چکیده

We prove analogues for elliptic interpolation functions of Macdonald’s version of the Littlewood identity for (skew) Macdonald polynomials, in the process developing an interpretation of general elliptic “hypergeometric” sums as skew interpolation functions. One such analogue has an interpretation as a “vanishing integral”, generalizing a result of [9]; the structure of this analogue gives sufficient insight to enable us to conjecture elliptic versions of most of the other vanishing integrals of [9] as well. We are thus led to formulate ten conjectures, each of which can be viewed as a multivariate quadratic transformation, and can be proved in a number of special cases.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Hall–littlewood Functions and the A2 Rogers–ramanujan Identities

We prove an identity for Hall–Littlewood symmetric functions labelled by the Lie algebra A2. Through specialization this yields a simple proof of the A2 Rogers–Ramanujan identities of Andrews, Schilling and the author. Nous démontrons une identité pour les functions symétriques de Hall–Littlewood associée à l’algèbre de Lie A2. En spécialisant cette identité, nous obtenons une démonstration sim...

متن کامل

A generalization of Kawanaka’s identity for Hall-Littlewood polynomials and applications

Recently, starting from two infinite summation formulae for Hall-Littlewood polynomials, two of the present authors [7] have generalized a method due to Macdonald [9] to obtain new finite summation formulae for these polynomials. This approach permits them to extend Stembridge’s list of multiple qseries identities of Rogers-Ramanujan type [12]. Conversely these symmetric functions identities ca...

متن کامل

New Identities of Hall-Littlewood Polynomials and Rogers-Ramanujan Type

where a = 0 or 1, are among the most famous q-series identities in partitions and combinatorics. Since their discovery the Rogers-Ramanujan identities have been proved and generalized in various ways (see [2, 4, 5, 13] and the references cited there). In [13], by adapting a method of Macdonald for calculating partial fraction expansions of symmetric formal power series, Stembridge gave an unusu...

متن کامل

Some Identities Involving Convolutions of Dirichlet Characters and the Möbius Function

In this paper we present some identities involving convolutions of Dirichlet characters and the Möbius function, which are related to a well known identity of Ramanujan, Hardy and Littlewood.

متن کامل

Local Identities Involving Jacobi Elliptic Functions

We derive a number of local identities of arbitrary rank involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclic identities discovered by us recently, along with an extension to several new cyclic identities of arbitrary rank. Second, we obtain a generalization to cyclic identities in which successive ter...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 119  شماره 

صفحات  -

تاریخ انتشار 2012