ar X iv : m at h / 99 10 14 8 v 1 [ m at h . A P ] 2 7 O ct 1 99 9 RELATIVE ZETA DETERMINANTS AND THE QUILLEN METRIC

نویسنده

  • SIMON SCOTT
چکیده

We compute the relation between the Quillen metric and and the canonical metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we present a general formula relating the ζdeterminant and the canonical determinant for a class of higher-order elliptic boundary value problems.

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

ar X iv : 0 81 0 . 16 21 v 1 [ m at h . Q A ] 9 O ct 2 00 8 DRINFEL ’ D DOUBLES AND SHAPOVALOV DETERMINANTS

The Shapovalov determinant for a class of pointed Hopf algebras is calculated, including quantized enveloping algebras, Lusztig’s small quantum groups, and quantized Lie superalgebras. Our main tools are root systems, Weyl groupoids, and Lusztig type isomorphisms. We elaborate powerful novel techniques for the algebras at roots of unity, and pass to the general case using a density argument.

متن کامل

ar X iv : m at h . R T / 0 11 13 06 v 1 2 9 N ov 2 00 1 CARTAN DETERMINANTS AND SHAPOVALOV FORMS

We compute the determinant of the Gram matrix of the Shapovalov form on weight spaces of the basic representation of an affine Kac-Moody algebra of ADE type (possibly twisted). As a consequence, we obtain explicit formulae for the determinants of the Cartan matrices of p-blocks of the symmetric group and its double cover, and of the associated Hecke algebras at roots of unity.

متن کامل

ar X iv : h ep - t h / 93 03 02 0 v 1 3 M ar 1 99 3 van Vleck determinants : geodesic focussing and defocussing in Lorentzian spacetimes

The van Vleck determinant is an ubiquitous object, arising in many physically interesting situations such as: (1) WKB approximations to quantum time evolution operators and Green functions. (2) Adiabatic approximations to heat kernels. (3) One loop approximations to functional integrals. (4) The theory of caustics in geometrical optics and ultrason-ics. (5) The focussing and defocussing of geod...

متن کامل

ar X iv : g r - qc / 9 31 10 23 v 1 1 4 N ov 1 99 3 Tunnelling geometries II . Reduction methods for functional determinants

The reduction algorithms for functional determinants of differential operators on spacetime manifolds of different topological types are presented, which were recently used for the calculation of the no-boundary wavefunction and the partition function of tunnelling geometries in quantum gravity and cosmology. PACS numbers: 04.60.+n, 03.70.+k, 98.80.Hw

متن کامل

ar X iv : m at h - ph / 0 11 10 07 v 1 5 N ov 2 00 1 FREDHOLM DETERMINANTS , JIMBO - MIWA - UENO TAU - FUNCTIONS , AND REPRESENTATION THEORY

The authors show that a wide class of Fredholm determinants arising in the representation theory of " big " groups such as the infinite–dimensional unitary group, solve Painlevé equations. Their methods are based on the theory of integrable operators and the theory of Riemann–Hilbert problems.

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999