The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive ...The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive power of this theory is rather limited. Furthermore, there are concerns that this theory will make it impossible to calculate some measured quantities, such as the masses of quarks and the electron. In this paper, we will show that a new development in string theory, the universal wave function interpretation of string theory, provides a way to derive the mathematical expression of the multiverse. We will demonstrate that the Weyl invariance existing in string theory indicates that our observed universe is a projection from a hologram. We will present how the laws of physics can be derived from this fact. Furthermore, we suggest it may also provide a way to calculate the masses of fundamental particles such as quarks and the electron.展开更多
This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applic...This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.展开更多
文摘The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive power of this theory is rather limited. Furthermore, there are concerns that this theory will make it impossible to calculate some measured quantities, such as the masses of quarks and the electron. In this paper, we will show that a new development in string theory, the universal wave function interpretation of string theory, provides a way to derive the mathematical expression of the multiverse. We will demonstrate that the Weyl invariance existing in string theory indicates that our observed universe is a projection from a hologram. We will present how the laws of physics can be derived from this fact. Furthermore, we suggest it may also provide a way to calculate the masses of fundamental particles such as quarks and the electron.
基金supported by a 2017 University of New South Wales Science Goldstar Grant(Jie Du)the Simons Foundation(Grant Nos. #359360(Brian Parshall) and #359363 (Leonard Scott))
文摘This paper aims at developing a "local-global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the cross-characteristic representation theory of finite groups of Lie type. We first review the notions of quasi-hereditary and stratified algebras over a Noetherian commutative ring. We prove that many global properties of these algebras hold if and only if they hold locally at every prime ideal. When the commutative ring is sufficiently good, it is often sufficient to check just the prime ideals of height at most one. These methods are applied to construct certain generalized q-Schur algebras, proving they are often quasi-hereditary(the "good" prime case) but always stratified. Finally, these results are used to prove a triangular decomposition matrix theorem for the modular representations of Hecke algebras at good primes. In the bad prime case, the generalized q-Schur algebras are at least stratified, and a block triangular analogue of the good prime case is proved, where the blocks correspond to Kazhdan-Lusztig cells.
