On parity functions in conformal field theories

We examine general aspects of parity functions arising in rational conformal field theories, as a result of Galois theoretic properties of modular transformations. We focus more specifically on parity functions associated with affine Lie algebras, for which we give two efficient formulas. We investigate the consequences of these for the modular invariance problem.Comment: 18 pages, no figure, LaTeX2

Symmetries of the Kac-Peterson Modular Matrices of Affine Algebras

The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define in a natural way a representation $R$ of the modular group $SL_2(Z)$. The matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular matrices, and describe the modular behaviour of the characters. In this paper we consider all levels of $(A_{r_1}\oplus\cdots\oplus A_{r_s})^{(1)}$, and for each of these find all permutations of the highest weights which commute with the corresponding Kac-Peterson matrices. This problem is equivalent to the classification of automorphism invariants of conformal field theories, and its solution, especially considering its simplicity, is a major step toward the classification of all Wess-Zumino-Witten conformal field theories.Comment: 16 pp, plain te

Staying in place during times of change in Arctic Alaska: The implications of attachment,alternatives, and buffering

The relationship between stability and change in social-ecological systems has received considerable attention in recent years, including the expectation that significant environmental changes will drive observable consequences for individuals, communities, and populations. Migration, as one example of response to adverse economic or environmental changes, has been observed in many places, including parts of the Far North. In Arctic Alaska, a relative lack of demographic or migratory response to rapid environmental and other changes has been observed. To understand why Arctic Alaska appears different, we draw on the literature on environmentally driven migration, focusing on three mechanisms that could account for the lack of response: attachment, the desire to remain in place, or the inability to relocate successfully; alternatives, ways to achieve similar outcomes through different means; and buffering, the reliance on subsidies or use of reserves to delay impacts. Each explanation has different implications for research and policy, indicating a need to further explore the relative contribution that each makes to a given situation in order to develop more effective responses locally and regionally. Given that the Arctic is on the front lines of climate change, these explanations are likely relevant to the ways changes play out in other parts of the world. Our review also underscores the importance of further attention to the details of social dynamics in climate change impacts and responses